Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
169 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
45 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Bit catastrophes for the Burrows-Wheeler Transform (2404.10426v2)

Published 16 Apr 2024 in cs.DS and cs.DM

Abstract: A bit catastrophe, loosely defined, is when a change in just one character of a string causes a significant change in the size of the compressed string. We study this phenomenon for the Burrows-Wheeler Transform (BWT), a string transform at the heart of several of the most popular compressors and aligners today. The parameter determining the size of the compressed data is the number of equal-letter runs of the BWT, commonly denoted $r$. We exhibit infinite families of strings in which insertion, deletion, resp. substitution of one character increases $r$ from constant to $\Theta(\log n)$, where $n$ is the length of the string. These strings can be interpreted both as examples for an increase by a multiplicative or an additive $\Theta(\log n)$-factor. As regards multiplicative factor, they attain the upper bound given by Akagi, Funakoshi, and Inenaga [Inf & Comput. 2023] of $O(\log n \log r)$, since here $r=O(1)$. We then give examples of strings in which insertion, deletion, resp. substitution of a character increases $r$ by a $\Theta(\sqrt{n})$ additive factor. These strings significantly improve the best known lower bound for an additive factor of $\Omega(\log n)$ [Giuliani et al., SOFSEM 2021].

Definition Search Book Streamline Icon: https://streamlinehq.com
References (33)
  1. Sensitivity of string compressors and repetitiveness measures. Information and Computation 291: 104999 . Bannai et al. [2020] Bannai, H., T. Gagie, and T. I. 2020. Refining the r-index. Theor. Comput. Sci. 812: 96–108 . Berstel and de Luca [1997] Berstel, J. and A. de Luca. 1997. Sturmian words, Lyndon words and trees. Theoretical Computer Science 178(1-2): 171–203 . Boucher et al. [2021] Boucher, C., D. Cenzato, Zs. Lipták, M. Rossi, and M. Sciortino 2021. r𝑟ritalic_r-indexing the eBWT. In T. Lecroq and H. Touzet (Eds.), Proc. of 28th International Symposium on String Processing and Information Retrieval (SPIRE 2021), Volume 12944 of Lecture Notes in Computer Science, pp.  3–12. Springer. Boucher et al. [2024] Boucher, C., D. Cenzato, Zs. Lipták, M. Rossi, and M. Sciortino. 2024. r𝑟ritalic_r-indexing the eBWT. Information and Computation 298: 105155. 10.1016/j.ic.2024.105155 . Brlek et al. [2019] Brlek, S., A. Frosini, I. Mancini, E. Pergola, and S. Rinaldi 2019. Burrows-Wheeler Transform of Words Defined by Morphisms. In IWOCA, Volume 11638 of Lect. Notes Comput. Sci., pp.  393–404. Springer. Burrows and Wheeler [1994] Burrows, M. and D.J. Wheeler 1994. A block-sorting lossless data compression algorithm. Technical report, DIGITAL System Research Center. Castiglione et al. [2010] Castiglione, G., A. Restivo, and M. Sciortino. 2010. On extremal cases of Hopcroft’s algorithm. Theoret. Comput. Sci. 411(38-39): 3414–3422 . de Luca [1997] de Luca, A. 1997. Sturmian words: Structure, combinatorics, and their arithmetics. Theor. Comput. Sci. 183(1): 45–82 . de Luca and Mignosi [1994] de Luca, A. and F. Mignosi. 1994. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Bannai, H., T. Gagie, and T. I. 2020. Refining the r-index. Theor. Comput. Sci. 812: 96–108 . Berstel and de Luca [1997] Berstel, J. and A. de Luca. 1997. Sturmian words, Lyndon words and trees. Theoretical Computer Science 178(1-2): 171–203 . Boucher et al. [2021] Boucher, C., D. Cenzato, Zs. Lipták, M. Rossi, and M. Sciortino 2021. r𝑟ritalic_r-indexing the eBWT. In T. Lecroq and H. Touzet (Eds.), Proc. of 28th International Symposium on String Processing and Information Retrieval (SPIRE 2021), Volume 12944 of Lecture Notes in Computer Science, pp.  3–12. Springer. Boucher et al. [2024] Boucher, C., D. Cenzato, Zs. Lipták, M. Rossi, and M. Sciortino. 2024. r𝑟ritalic_r-indexing the eBWT. Information and Computation 298: 105155. 10.1016/j.ic.2024.105155 . Brlek et al. [2019] Brlek, S., A. Frosini, I. Mancini, E. Pergola, and S. Rinaldi 2019. Burrows-Wheeler Transform of Words Defined by Morphisms. In IWOCA, Volume 11638 of Lect. Notes Comput. Sci., pp.  393–404. Springer. Burrows and Wheeler [1994] Burrows, M. and D.J. Wheeler 1994. A block-sorting lossless data compression algorithm. Technical report, DIGITAL System Research Center. Castiglione et al. [2010] Castiglione, G., A. Restivo, and M. Sciortino. 2010. On extremal cases of Hopcroft’s algorithm. Theoret. Comput. Sci. 411(38-39): 3414–3422 . de Luca [1997] de Luca, A. 1997. Sturmian words: Structure, combinatorics, and their arithmetics. Theor. Comput. Sci. 183(1): 45–82 . de Luca and Mignosi [1994] de Luca, A. and F. Mignosi. 1994. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Berstel, J. and A. de Luca. 1997. Sturmian words, Lyndon words and trees. Theoretical Computer Science 178(1-2): 171–203 . Boucher et al. [2021] Boucher, C., D. Cenzato, Zs. Lipták, M. Rossi, and M. Sciortino 2021. r𝑟ritalic_r-indexing the eBWT. In T. Lecroq and H. Touzet (Eds.), Proc. of 28th International Symposium on String Processing and Information Retrieval (SPIRE 2021), Volume 12944 of Lecture Notes in Computer Science, pp.  3–12. Springer. Boucher et al. [2024] Boucher, C., D. Cenzato, Zs. Lipták, M. Rossi, and M. Sciortino. 2024. r𝑟ritalic_r-indexing the eBWT. Information and Computation 298: 105155. 10.1016/j.ic.2024.105155 . Brlek et al. [2019] Brlek, S., A. Frosini, I. Mancini, E. Pergola, and S. Rinaldi 2019. Burrows-Wheeler Transform of Words Defined by Morphisms. In IWOCA, Volume 11638 of Lect. Notes Comput. Sci., pp.  393–404. Springer. Burrows and Wheeler [1994] Burrows, M. and D.J. Wheeler 1994. A block-sorting lossless data compression algorithm. Technical report, DIGITAL System Research Center. Castiglione et al. [2010] Castiglione, G., A. Restivo, and M. Sciortino. 2010. On extremal cases of Hopcroft’s algorithm. Theoret. Comput. Sci. 411(38-39): 3414–3422 . de Luca [1997] de Luca, A. 1997. Sturmian words: Structure, combinatorics, and their arithmetics. Theor. Comput. Sci. 183(1): 45–82 . de Luca and Mignosi [1994] de Luca, A. and F. Mignosi. 1994. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Boucher, C., D. Cenzato, Zs. Lipták, M. Rossi, and M. Sciortino 2021. r𝑟ritalic_r-indexing the eBWT. In T. Lecroq and H. Touzet (Eds.), Proc. of 28th International Symposium on String Processing and Information Retrieval (SPIRE 2021), Volume 12944 of Lecture Notes in Computer Science, pp.  3–12. Springer. Boucher et al. [2024] Boucher, C., D. Cenzato, Zs. Lipták, M. Rossi, and M. Sciortino. 2024. r𝑟ritalic_r-indexing the eBWT. Information and Computation 298: 105155. 10.1016/j.ic.2024.105155 . Brlek et al. [2019] Brlek, S., A. Frosini, I. Mancini, E. Pergola, and S. Rinaldi 2019. Burrows-Wheeler Transform of Words Defined by Morphisms. In IWOCA, Volume 11638 of Lect. Notes Comput. Sci., pp.  393–404. Springer. Burrows and Wheeler [1994] Burrows, M. and D.J. Wheeler 1994. A block-sorting lossless data compression algorithm. Technical report, DIGITAL System Research Center. Castiglione et al. [2010] Castiglione, G., A. Restivo, and M. Sciortino. 2010. On extremal cases of Hopcroft’s algorithm. Theoret. Comput. Sci. 411(38-39): 3414–3422 . de Luca [1997] de Luca, A. 1997. Sturmian words: Structure, combinatorics, and their arithmetics. Theor. Comput. Sci. 183(1): 45–82 . de Luca and Mignosi [1994] de Luca, A. and F. Mignosi. 1994. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Boucher, C., D. Cenzato, Zs. Lipták, M. Rossi, and M. Sciortino. 2024. r𝑟ritalic_r-indexing the eBWT. Information and Computation 298: 105155. 10.1016/j.ic.2024.105155 . Brlek et al. [2019] Brlek, S., A. Frosini, I. Mancini, E. Pergola, and S. Rinaldi 2019. Burrows-Wheeler Transform of Words Defined by Morphisms. In IWOCA, Volume 11638 of Lect. Notes Comput. Sci., pp.  393–404. Springer. Burrows and Wheeler [1994] Burrows, M. and D.J. Wheeler 1994. A block-sorting lossless data compression algorithm. Technical report, DIGITAL System Research Center. Castiglione et al. [2010] Castiglione, G., A. Restivo, and M. Sciortino. 2010. On extremal cases of Hopcroft’s algorithm. Theoret. Comput. Sci. 411(38-39): 3414–3422 . de Luca [1997] de Luca, A. 1997. Sturmian words: Structure, combinatorics, and their arithmetics. Theor. Comput. Sci. 183(1): 45–82 . de Luca and Mignosi [1994] de Luca, A. and F. Mignosi. 1994. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Brlek, S., A. Frosini, I. Mancini, E. Pergola, and S. Rinaldi 2019. Burrows-Wheeler Transform of Words Defined by Morphisms. In IWOCA, Volume 11638 of Lect. Notes Comput. Sci., pp.  393–404. Springer. Burrows and Wheeler [1994] Burrows, M. and D.J. Wheeler 1994. A block-sorting lossless data compression algorithm. Technical report, DIGITAL System Research Center. Castiglione et al. [2010] Castiglione, G., A. Restivo, and M. Sciortino. 2010. On extremal cases of Hopcroft’s algorithm. Theoret. Comput. Sci. 411(38-39): 3414–3422 . de Luca [1997] de Luca, A. 1997. Sturmian words: Structure, combinatorics, and their arithmetics. Theor. Comput. Sci. 183(1): 45–82 . de Luca and Mignosi [1994] de Luca, A. and F. Mignosi. 1994. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Burrows, M. and D.J. Wheeler 1994. A block-sorting lossless data compression algorithm. Technical report, DIGITAL System Research Center. Castiglione et al. [2010] Castiglione, G., A. Restivo, and M. Sciortino. 2010. On extremal cases of Hopcroft’s algorithm. Theoret. Comput. Sci. 411(38-39): 3414–3422 . de Luca [1997] de Luca, A. 1997. Sturmian words: Structure, combinatorics, and their arithmetics. Theor. Comput. Sci. 183(1): 45–82 . de Luca and Mignosi [1994] de Luca, A. and F. Mignosi. 1994. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Castiglione, G., A. Restivo, and M. Sciortino. 2010. On extremal cases of Hopcroft’s algorithm. Theoret. Comput. Sci. 411(38-39): 3414–3422 . de Luca [1997] de Luca, A. 1997. Sturmian words: Structure, combinatorics, and their arithmetics. Theor. Comput. Sci. 183(1): 45–82 . de Luca and Mignosi [1994] de Luca, A. and F. Mignosi. 1994. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . de Luca, A. 1997. Sturmian words: Structure, combinatorics, and their arithmetics. Theor. Comput. Sci. 183(1): 45–82 . de Luca and Mignosi [1994] de Luca, A. and F. Mignosi. 1994. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . de Luca, A. and F. Mignosi. 1994. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 .
  2. Refining the r-index. Theor. Comput. Sci. 812: 96–108 . Berstel and de Luca [1997] Berstel, J. and A. de Luca. 1997. Sturmian words, Lyndon words and trees. Theoretical Computer Science 178(1-2): 171–203 . Boucher et al. [2021] Boucher, C., D. Cenzato, Zs. Lipták, M. Rossi, and M. Sciortino 2021. r𝑟ritalic_r-indexing the eBWT. In T. Lecroq and H. Touzet (Eds.), Proc. of 28th International Symposium on String Processing and Information Retrieval (SPIRE 2021), Volume 12944 of Lecture Notes in Computer Science, pp.  3–12. Springer. Boucher et al. [2024] Boucher, C., D. Cenzato, Zs. Lipták, M. Rossi, and M. Sciortino. 2024. r𝑟ritalic_r-indexing the eBWT. Information and Computation 298: 105155. 10.1016/j.ic.2024.105155 . Brlek et al. [2019] Brlek, S., A. Frosini, I. Mancini, E. Pergola, and S. Rinaldi 2019. Burrows-Wheeler Transform of Words Defined by Morphisms. In IWOCA, Volume 11638 of Lect. Notes Comput. Sci., pp.  393–404. Springer. Burrows and Wheeler [1994] Burrows, M. and D.J. Wheeler 1994. A block-sorting lossless data compression algorithm. Technical report, DIGITAL System Research Center. Castiglione et al. [2010] Castiglione, G., A. Restivo, and M. Sciortino. 2010. On extremal cases of Hopcroft’s algorithm. Theoret. Comput. Sci. 411(38-39): 3414–3422 . de Luca [1997] de Luca, A. 1997. Sturmian words: Structure, combinatorics, and their arithmetics. Theor. Comput. Sci. 183(1): 45–82 . de Luca and Mignosi [1994] de Luca, A. and F. Mignosi. 1994. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Berstel, J. and A. de Luca. 1997. Sturmian words, Lyndon words and trees. Theoretical Computer Science 178(1-2): 171–203 . Boucher et al. [2021] Boucher, C., D. Cenzato, Zs. Lipták, M. Rossi, and M. Sciortino 2021. r𝑟ritalic_r-indexing the eBWT. In T. Lecroq and H. Touzet (Eds.), Proc. of 28th International Symposium on String Processing and Information Retrieval (SPIRE 2021), Volume 12944 of Lecture Notes in Computer Science, pp.  3–12. Springer. Boucher et al. [2024] Boucher, C., D. Cenzato, Zs. Lipták, M. Rossi, and M. Sciortino. 2024. r𝑟ritalic_r-indexing the eBWT. Information and Computation 298: 105155. 10.1016/j.ic.2024.105155 . Brlek et al. [2019] Brlek, S., A. Frosini, I. Mancini, E. Pergola, and S. Rinaldi 2019. Burrows-Wheeler Transform of Words Defined by Morphisms. In IWOCA, Volume 11638 of Lect. Notes Comput. Sci., pp.  393–404. Springer. Burrows and Wheeler [1994] Burrows, M. and D.J. Wheeler 1994. A block-sorting lossless data compression algorithm. Technical report, DIGITAL System Research Center. Castiglione et al. [2010] Castiglione, G., A. Restivo, and M. Sciortino. 2010. On extremal cases of Hopcroft’s algorithm. Theoret. Comput. Sci. 411(38-39): 3414–3422 . de Luca [1997] de Luca, A. 1997. Sturmian words: Structure, combinatorics, and their arithmetics. Theor. Comput. Sci. 183(1): 45–82 . de Luca and Mignosi [1994] de Luca, A. and F. Mignosi. 1994. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Boucher, C., D. Cenzato, Zs. Lipták, M. Rossi, and M. Sciortino 2021. r𝑟ritalic_r-indexing the eBWT. In T. Lecroq and H. Touzet (Eds.), Proc. of 28th International Symposium on String Processing and Information Retrieval (SPIRE 2021), Volume 12944 of Lecture Notes in Computer Science, pp.  3–12. Springer. Boucher et al. [2024] Boucher, C., D. Cenzato, Zs. Lipták, M. Rossi, and M. Sciortino. 2024. r𝑟ritalic_r-indexing the eBWT. Information and Computation 298: 105155. 10.1016/j.ic.2024.105155 . Brlek et al. [2019] Brlek, S., A. Frosini, I. Mancini, E. Pergola, and S. Rinaldi 2019. Burrows-Wheeler Transform of Words Defined by Morphisms. In IWOCA, Volume 11638 of Lect. Notes Comput. Sci., pp.  393–404. Springer. Burrows and Wheeler [1994] Burrows, M. and D.J. Wheeler 1994. A block-sorting lossless data compression algorithm. Technical report, DIGITAL System Research Center. Castiglione et al. [2010] Castiglione, G., A. Restivo, and M. Sciortino. 2010. On extremal cases of Hopcroft’s algorithm. Theoret. Comput. Sci. 411(38-39): 3414–3422 . de Luca [1997] de Luca, A. 1997. Sturmian words: Structure, combinatorics, and their arithmetics. Theor. Comput. Sci. 183(1): 45–82 . de Luca and Mignosi [1994] de Luca, A. and F. Mignosi. 1994. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Boucher, C., D. Cenzato, Zs. Lipták, M. Rossi, and M. Sciortino. 2024. r𝑟ritalic_r-indexing the eBWT. Information and Computation 298: 105155. 10.1016/j.ic.2024.105155 . Brlek et al. [2019] Brlek, S., A. Frosini, I. Mancini, E. Pergola, and S. Rinaldi 2019. Burrows-Wheeler Transform of Words Defined by Morphisms. In IWOCA, Volume 11638 of Lect. Notes Comput. Sci., pp.  393–404. Springer. Burrows and Wheeler [1994] Burrows, M. and D.J. Wheeler 1994. A block-sorting lossless data compression algorithm. Technical report, DIGITAL System Research Center. Castiglione et al. [2010] Castiglione, G., A. Restivo, and M. Sciortino. 2010. On extremal cases of Hopcroft’s algorithm. Theoret. Comput. Sci. 411(38-39): 3414–3422 . de Luca [1997] de Luca, A. 1997. Sturmian words: Structure, combinatorics, and their arithmetics. Theor. Comput. Sci. 183(1): 45–82 . de Luca and Mignosi [1994] de Luca, A. and F. Mignosi. 1994. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Brlek, S., A. Frosini, I. Mancini, E. Pergola, and S. Rinaldi 2019. Burrows-Wheeler Transform of Words Defined by Morphisms. In IWOCA, Volume 11638 of Lect. Notes Comput. Sci., pp.  393–404. Springer. Burrows and Wheeler [1994] Burrows, M. and D.J. Wheeler 1994. A block-sorting lossless data compression algorithm. Technical report, DIGITAL System Research Center. Castiglione et al. [2010] Castiglione, G., A. Restivo, and M. Sciortino. 2010. On extremal cases of Hopcroft’s algorithm. Theoret. Comput. Sci. 411(38-39): 3414–3422 . de Luca [1997] de Luca, A. 1997. Sturmian words: Structure, combinatorics, and their arithmetics. Theor. Comput. Sci. 183(1): 45–82 . de Luca and Mignosi [1994] de Luca, A. and F. Mignosi. 1994. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Burrows, M. and D.J. Wheeler 1994. A block-sorting lossless data compression algorithm. Technical report, DIGITAL System Research Center. Castiglione et al. [2010] Castiglione, G., A. Restivo, and M. Sciortino. 2010. On extremal cases of Hopcroft’s algorithm. Theoret. Comput. Sci. 411(38-39): 3414–3422 . de Luca [1997] de Luca, A. 1997. Sturmian words: Structure, combinatorics, and their arithmetics. Theor. Comput. Sci. 183(1): 45–82 . de Luca and Mignosi [1994] de Luca, A. and F. Mignosi. 1994. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Castiglione, G., A. Restivo, and M. Sciortino. 2010. On extremal cases of Hopcroft’s algorithm. Theoret. Comput. Sci. 411(38-39): 3414–3422 . de Luca [1997] de Luca, A. 1997. Sturmian words: Structure, combinatorics, and their arithmetics. Theor. Comput. Sci. 183(1): 45–82 . de Luca and Mignosi [1994] de Luca, A. and F. Mignosi. 1994. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . de Luca, A. 1997. Sturmian words: Structure, combinatorics, and their arithmetics. Theor. Comput. Sci. 183(1): 45–82 . de Luca and Mignosi [1994] de Luca, A. and F. Mignosi. 1994. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . de Luca, A. and F. Mignosi. 1994. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 .
  3. Sturmian words, Lyndon words and trees. Theoretical Computer Science 178(1-2): 171–203 . Boucher et al. [2021] Boucher, C., D. Cenzato, Zs. Lipták, M. Rossi, and M. Sciortino 2021. r𝑟ritalic_r-indexing the eBWT. In T. Lecroq and H. Touzet (Eds.), Proc. of 28th International Symposium on String Processing and Information Retrieval (SPIRE 2021), Volume 12944 of Lecture Notes in Computer Science, pp.  3–12. Springer. Boucher et al. [2024] Boucher, C., D. Cenzato, Zs. Lipták, M. Rossi, and M. Sciortino. 2024. r𝑟ritalic_r-indexing the eBWT. Information and Computation 298: 105155. 10.1016/j.ic.2024.105155 . Brlek et al. [2019] Brlek, S., A. Frosini, I. Mancini, E. Pergola, and S. Rinaldi 2019. Burrows-Wheeler Transform of Words Defined by Morphisms. In IWOCA, Volume 11638 of Lect. Notes Comput. Sci., pp.  393–404. Springer. Burrows and Wheeler [1994] Burrows, M. and D.J. Wheeler 1994. A block-sorting lossless data compression algorithm. Technical report, DIGITAL System Research Center. Castiglione et al. [2010] Castiglione, G., A. Restivo, and M. Sciortino. 2010. On extremal cases of Hopcroft’s algorithm. Theoret. Comput. Sci. 411(38-39): 3414–3422 . de Luca [1997] de Luca, A. 1997. Sturmian words: Structure, combinatorics, and their arithmetics. Theor. Comput. Sci. 183(1): 45–82 . de Luca and Mignosi [1994] de Luca, A. and F. Mignosi. 1994. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Boucher, C., D. Cenzato, Zs. Lipták, M. Rossi, and M. Sciortino 2021. r𝑟ritalic_r-indexing the eBWT. In T. Lecroq and H. Touzet (Eds.), Proc. of 28th International Symposium on String Processing and Information Retrieval (SPIRE 2021), Volume 12944 of Lecture Notes in Computer Science, pp.  3–12. Springer. Boucher et al. [2024] Boucher, C., D. Cenzato, Zs. Lipták, M. Rossi, and M. Sciortino. 2024. r𝑟ritalic_r-indexing the eBWT. Information and Computation 298: 105155. 10.1016/j.ic.2024.105155 . Brlek et al. [2019] Brlek, S., A. Frosini, I. Mancini, E. Pergola, and S. Rinaldi 2019. Burrows-Wheeler Transform of Words Defined by Morphisms. In IWOCA, Volume 11638 of Lect. Notes Comput. Sci., pp.  393–404. Springer. Burrows and Wheeler [1994] Burrows, M. and D.J. Wheeler 1994. A block-sorting lossless data compression algorithm. Technical report, DIGITAL System Research Center. Castiglione et al. [2010] Castiglione, G., A. Restivo, and M. Sciortino. 2010. On extremal cases of Hopcroft’s algorithm. Theoret. Comput. Sci. 411(38-39): 3414–3422 . de Luca [1997] de Luca, A. 1997. Sturmian words: Structure, combinatorics, and their arithmetics. Theor. Comput. Sci. 183(1): 45–82 . de Luca and Mignosi [1994] de Luca, A. and F. Mignosi. 1994. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Boucher, C., D. Cenzato, Zs. Lipták, M. Rossi, and M. Sciortino. 2024. r𝑟ritalic_r-indexing the eBWT. Information and Computation 298: 105155. 10.1016/j.ic.2024.105155 . Brlek et al. [2019] Brlek, S., A. Frosini, I. Mancini, E. Pergola, and S. Rinaldi 2019. Burrows-Wheeler Transform of Words Defined by Morphisms. In IWOCA, Volume 11638 of Lect. Notes Comput. Sci., pp.  393–404. Springer. Burrows and Wheeler [1994] Burrows, M. and D.J. Wheeler 1994. A block-sorting lossless data compression algorithm. Technical report, DIGITAL System Research Center. Castiglione et al. [2010] Castiglione, G., A. Restivo, and M. Sciortino. 2010. On extremal cases of Hopcroft’s algorithm. Theoret. Comput. Sci. 411(38-39): 3414–3422 . de Luca [1997] de Luca, A. 1997. Sturmian words: Structure, combinatorics, and their arithmetics. Theor. Comput. Sci. 183(1): 45–82 . de Luca and Mignosi [1994] de Luca, A. and F. Mignosi. 1994. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Brlek, S., A. Frosini, I. Mancini, E. Pergola, and S. Rinaldi 2019. Burrows-Wheeler Transform of Words Defined by Morphisms. In IWOCA, Volume 11638 of Lect. Notes Comput. Sci., pp.  393–404. Springer. Burrows and Wheeler [1994] Burrows, M. and D.J. Wheeler 1994. A block-sorting lossless data compression algorithm. Technical report, DIGITAL System Research Center. Castiglione et al. [2010] Castiglione, G., A. Restivo, and M. Sciortino. 2010. On extremal cases of Hopcroft’s algorithm. Theoret. Comput. Sci. 411(38-39): 3414–3422 . de Luca [1997] de Luca, A. 1997. Sturmian words: Structure, combinatorics, and their arithmetics. Theor. Comput. Sci. 183(1): 45–82 . de Luca and Mignosi [1994] de Luca, A. and F. Mignosi. 1994. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Burrows, M. and D.J. Wheeler 1994. A block-sorting lossless data compression algorithm. Technical report, DIGITAL System Research Center. Castiglione et al. [2010] Castiglione, G., A. Restivo, and M. Sciortino. 2010. On extremal cases of Hopcroft’s algorithm. Theoret. Comput. Sci. 411(38-39): 3414–3422 . de Luca [1997] de Luca, A. 1997. Sturmian words: Structure, combinatorics, and their arithmetics. Theor. Comput. Sci. 183(1): 45–82 . de Luca and Mignosi [1994] de Luca, A. and F. Mignosi. 1994. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Castiglione, G., A. Restivo, and M. Sciortino. 2010. On extremal cases of Hopcroft’s algorithm. Theoret. Comput. Sci. 411(38-39): 3414–3422 . de Luca [1997] de Luca, A. 1997. Sturmian words: Structure, combinatorics, and their arithmetics. Theor. Comput. Sci. 183(1): 45–82 . de Luca and Mignosi [1994] de Luca, A. and F. Mignosi. 1994. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . de Luca, A. 1997. Sturmian words: Structure, combinatorics, and their arithmetics. Theor. Comput. Sci. 183(1): 45–82 . de Luca and Mignosi [1994] de Luca, A. and F. Mignosi. 1994. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . de Luca, A. and F. Mignosi. 1994. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 .
  4. r𝑟ritalic_r-indexing the eBWT. In T. Lecroq and H. Touzet (Eds.), Proc. of 28th International Symposium on String Processing and Information Retrieval (SPIRE 2021), Volume 12944 of Lecture Notes in Computer Science, pp.  3–12. Springer. Boucher et al. [2024] Boucher, C., D. Cenzato, Zs. Lipták, M. Rossi, and M. Sciortino. 2024. r𝑟ritalic_r-indexing the eBWT. Information and Computation 298: 105155. 10.1016/j.ic.2024.105155 . Brlek et al. [2019] Brlek, S., A. Frosini, I. Mancini, E. Pergola, and S. Rinaldi 2019. Burrows-Wheeler Transform of Words Defined by Morphisms. In IWOCA, Volume 11638 of Lect. Notes Comput. Sci., pp.  393–404. Springer. Burrows and Wheeler [1994] Burrows, M. and D.J. Wheeler 1994. A block-sorting lossless data compression algorithm. Technical report, DIGITAL System Research Center. Castiglione et al. [2010] Castiglione, G., A. Restivo, and M. Sciortino. 2010. On extremal cases of Hopcroft’s algorithm. Theoret. Comput. Sci. 411(38-39): 3414–3422 . de Luca [1997] de Luca, A. 1997. Sturmian words: Structure, combinatorics, and their arithmetics. Theor. Comput. Sci. 183(1): 45–82 . de Luca and Mignosi [1994] de Luca, A. and F. Mignosi. 1994. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Boucher, C., D. Cenzato, Zs. Lipták, M. Rossi, and M. Sciortino. 2024. r𝑟ritalic_r-indexing the eBWT. Information and Computation 298: 105155. 10.1016/j.ic.2024.105155 . Brlek et al. [2019] Brlek, S., A. Frosini, I. Mancini, E. Pergola, and S. Rinaldi 2019. Burrows-Wheeler Transform of Words Defined by Morphisms. In IWOCA, Volume 11638 of Lect. Notes Comput. Sci., pp.  393–404. Springer. Burrows and Wheeler [1994] Burrows, M. and D.J. Wheeler 1994. A block-sorting lossless data compression algorithm. Technical report, DIGITAL System Research Center. Castiglione et al. [2010] Castiglione, G., A. Restivo, and M. Sciortino. 2010. On extremal cases of Hopcroft’s algorithm. Theoret. Comput. Sci. 411(38-39): 3414–3422 . de Luca [1997] de Luca, A. 1997. Sturmian words: Structure, combinatorics, and their arithmetics. Theor. Comput. Sci. 183(1): 45–82 . de Luca and Mignosi [1994] de Luca, A. and F. Mignosi. 1994. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Brlek, S., A. Frosini, I. Mancini, E. Pergola, and S. Rinaldi 2019. Burrows-Wheeler Transform of Words Defined by Morphisms. In IWOCA, Volume 11638 of Lect. Notes Comput. Sci., pp.  393–404. Springer. Burrows and Wheeler [1994] Burrows, M. and D.J. Wheeler 1994. A block-sorting lossless data compression algorithm. Technical report, DIGITAL System Research Center. Castiglione et al. [2010] Castiglione, G., A. Restivo, and M. Sciortino. 2010. On extremal cases of Hopcroft’s algorithm. Theoret. Comput. Sci. 411(38-39): 3414–3422 . de Luca [1997] de Luca, A. 1997. Sturmian words: Structure, combinatorics, and their arithmetics. Theor. Comput. Sci. 183(1): 45–82 . de Luca and Mignosi [1994] de Luca, A. and F. Mignosi. 1994. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Burrows, M. and D.J. Wheeler 1994. A block-sorting lossless data compression algorithm. Technical report, DIGITAL System Research Center. Castiglione et al. [2010] Castiglione, G., A. Restivo, and M. Sciortino. 2010. On extremal cases of Hopcroft’s algorithm. Theoret. Comput. Sci. 411(38-39): 3414–3422 . de Luca [1997] de Luca, A. 1997. Sturmian words: Structure, combinatorics, and their arithmetics. Theor. Comput. Sci. 183(1): 45–82 . de Luca and Mignosi [1994] de Luca, A. and F. Mignosi. 1994. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Castiglione, G., A. Restivo, and M. Sciortino. 2010. On extremal cases of Hopcroft’s algorithm. Theoret. Comput. Sci. 411(38-39): 3414–3422 . de Luca [1997] de Luca, A. 1997. Sturmian words: Structure, combinatorics, and their arithmetics. Theor. Comput. Sci. 183(1): 45–82 . de Luca and Mignosi [1994] de Luca, A. and F. Mignosi. 1994. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . de Luca, A. 1997. Sturmian words: Structure, combinatorics, and their arithmetics. Theor. Comput. Sci. 183(1): 45–82 . de Luca and Mignosi [1994] de Luca, A. and F. Mignosi. 1994. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . de Luca, A. and F. Mignosi. 1994. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 .
  5. r𝑟ritalic_r-indexing the eBWT. Information and Computation 298: 105155. 10.1016/j.ic.2024.105155 . Brlek et al. [2019] Brlek, S., A. Frosini, I. Mancini, E. Pergola, and S. Rinaldi 2019. Burrows-Wheeler Transform of Words Defined by Morphisms. In IWOCA, Volume 11638 of Lect. Notes Comput. Sci., pp.  393–404. Springer. Burrows and Wheeler [1994] Burrows, M. and D.J. Wheeler 1994. A block-sorting lossless data compression algorithm. Technical report, DIGITAL System Research Center. Castiglione et al. [2010] Castiglione, G., A. Restivo, and M. Sciortino. 2010. On extremal cases of Hopcroft’s algorithm. Theoret. Comput. Sci. 411(38-39): 3414–3422 . de Luca [1997] de Luca, A. 1997. Sturmian words: Structure, combinatorics, and their arithmetics. Theor. Comput. Sci. 183(1): 45–82 . de Luca and Mignosi [1994] de Luca, A. and F. Mignosi. 1994. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Brlek, S., A. Frosini, I. Mancini, E. Pergola, and S. Rinaldi 2019. Burrows-Wheeler Transform of Words Defined by Morphisms. In IWOCA, Volume 11638 of Lect. Notes Comput. Sci., pp.  393–404. Springer. Burrows and Wheeler [1994] Burrows, M. and D.J. Wheeler 1994. A block-sorting lossless data compression algorithm. Technical report, DIGITAL System Research Center. Castiglione et al. [2010] Castiglione, G., A. Restivo, and M. Sciortino. 2010. On extremal cases of Hopcroft’s algorithm. Theoret. Comput. Sci. 411(38-39): 3414–3422 . de Luca [1997] de Luca, A. 1997. Sturmian words: Structure, combinatorics, and their arithmetics. Theor. Comput. Sci. 183(1): 45–82 . de Luca and Mignosi [1994] de Luca, A. and F. Mignosi. 1994. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Burrows, M. and D.J. Wheeler 1994. A block-sorting lossless data compression algorithm. Technical report, DIGITAL System Research Center. Castiglione et al. [2010] Castiglione, G., A. Restivo, and M. Sciortino. 2010. On extremal cases of Hopcroft’s algorithm. Theoret. Comput. Sci. 411(38-39): 3414–3422 . de Luca [1997] de Luca, A. 1997. Sturmian words: Structure, combinatorics, and their arithmetics. Theor. Comput. Sci. 183(1): 45–82 . de Luca and Mignosi [1994] de Luca, A. and F. Mignosi. 1994. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Castiglione, G., A. Restivo, and M. Sciortino. 2010. On extremal cases of Hopcroft’s algorithm. Theoret. Comput. Sci. 411(38-39): 3414–3422 . de Luca [1997] de Luca, A. 1997. Sturmian words: Structure, combinatorics, and their arithmetics. Theor. Comput. Sci. 183(1): 45–82 . de Luca and Mignosi [1994] de Luca, A. and F. Mignosi. 1994. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . de Luca, A. 1997. Sturmian words: Structure, combinatorics, and their arithmetics. Theor. Comput. Sci. 183(1): 45–82 . de Luca and Mignosi [1994] de Luca, A. and F. Mignosi. 1994. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . de Luca, A. and F. Mignosi. 1994. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 .
  6. Burrows-Wheeler Transform of Words Defined by Morphisms. In IWOCA, Volume 11638 of Lect. Notes Comput. Sci., pp.  393–404. Springer. Burrows and Wheeler [1994] Burrows, M. and D.J. Wheeler 1994. A block-sorting lossless data compression algorithm. Technical report, DIGITAL System Research Center. Castiglione et al. [2010] Castiglione, G., A. Restivo, and M. Sciortino. 2010. On extremal cases of Hopcroft’s algorithm. Theoret. Comput. Sci. 411(38-39): 3414–3422 . de Luca [1997] de Luca, A. 1997. Sturmian words: Structure, combinatorics, and their arithmetics. Theor. Comput. Sci. 183(1): 45–82 . de Luca and Mignosi [1994] de Luca, A. and F. Mignosi. 1994. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Burrows, M. and D.J. Wheeler 1994. A block-sorting lossless data compression algorithm. Technical report, DIGITAL System Research Center. Castiglione et al. [2010] Castiglione, G., A. Restivo, and M. Sciortino. 2010. On extremal cases of Hopcroft’s algorithm. Theoret. Comput. Sci. 411(38-39): 3414–3422 . de Luca [1997] de Luca, A. 1997. Sturmian words: Structure, combinatorics, and their arithmetics. Theor. Comput. Sci. 183(1): 45–82 . de Luca and Mignosi [1994] de Luca, A. and F. Mignosi. 1994. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Castiglione, G., A. Restivo, and M. Sciortino. 2010. On extremal cases of Hopcroft’s algorithm. Theoret. Comput. Sci. 411(38-39): 3414–3422 . de Luca [1997] de Luca, A. 1997. Sturmian words: Structure, combinatorics, and their arithmetics. Theor. Comput. Sci. 183(1): 45–82 . de Luca and Mignosi [1994] de Luca, A. and F. Mignosi. 1994. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . de Luca, A. 1997. Sturmian words: Structure, combinatorics, and their arithmetics. Theor. Comput. Sci. 183(1): 45–82 . de Luca and Mignosi [1994] de Luca, A. and F. Mignosi. 1994. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . de Luca, A. and F. Mignosi. 1994. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 .
  7. Burrows, M. and D.J. Wheeler 1994. A block-sorting lossless data compression algorithm. Technical report, DIGITAL System Research Center. Castiglione et al. [2010] Castiglione, G., A. Restivo, and M. Sciortino. 2010. On extremal cases of Hopcroft’s algorithm. Theoret. Comput. Sci. 411(38-39): 3414–3422 . de Luca [1997] de Luca, A. 1997. Sturmian words: Structure, combinatorics, and their arithmetics. Theor. Comput. Sci. 183(1): 45–82 . de Luca and Mignosi [1994] de Luca, A. and F. Mignosi. 1994. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Castiglione, G., A. Restivo, and M. Sciortino. 2010. On extremal cases of Hopcroft’s algorithm. Theoret. Comput. Sci. 411(38-39): 3414–3422 . de Luca [1997] de Luca, A. 1997. Sturmian words: Structure, combinatorics, and their arithmetics. Theor. Comput. Sci. 183(1): 45–82 . de Luca and Mignosi [1994] de Luca, A. and F. Mignosi. 1994. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . de Luca, A. 1997. Sturmian words: Structure, combinatorics, and their arithmetics. Theor. Comput. Sci. 183(1): 45–82 . de Luca and Mignosi [1994] de Luca, A. and F. Mignosi. 1994. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . de Luca, A. and F. Mignosi. 1994. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 .
  8. On extremal cases of Hopcroft’s algorithm. Theoret. Comput. Sci. 411(38-39): 3414–3422 . de Luca [1997] de Luca, A. 1997. Sturmian words: Structure, combinatorics, and their arithmetics. Theor. Comput. Sci. 183(1): 45–82 . de Luca and Mignosi [1994] de Luca, A. and F. Mignosi. 1994. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . de Luca, A. 1997. Sturmian words: Structure, combinatorics, and their arithmetics. Theor. Comput. Sci. 183(1): 45–82 . de Luca and Mignosi [1994] de Luca, A. and F. Mignosi. 1994. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . de Luca, A. and F. Mignosi. 1994. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 .
  9. de Luca, A. 1997. Sturmian words: Structure, combinatorics, and their arithmetics. Theor. Comput. Sci. 183(1): 45–82 . de Luca and Mignosi [1994] de Luca, A. and F. Mignosi. 1994. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . de Luca, A. and F. Mignosi. 1994. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 .
  10. Some Combinatorial Properties of Sturmian Words. Theor. Comput. Sci. 136(2): 361–285 . Ferragina and Manzini [2000] Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ferragina, P. and G. Manzini 2000. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 .
  11. Opportunistic data structures with applications. In FOCS, pp.  390–398. IEEE Computer Society. Frosini et al. [2022] Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Frosini, A., I. Mancini, S. Rinaldi, G. Romana, and M. Sciortino 2022. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 .
  12. Logarithmic equal-letter runs for BWT of purely morphic words. In DLT, Volume 13257 of Lect. Notes Comput. Sci., pp.  139–151. Springer. Gagie et al. [2018] Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Gagie, T., G. Navarro, and N. Prezza 2018. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 .
  13. Optimal-time text indexing in BWT-runs bounded space. In A. Czumaj (Ed.), SODA, pp.  1459–1477. SIAM. Gagie et al. [2020] Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Gagie, T., G. Navarro, and N. Prezza. 2020. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 .
  14. Fully functional suffix trees and optimal text searching in BWT-runs bounded space. J. ACM 67(1): 2:1–2:54 . Giuliani et al. [2021] Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Giuliani, S., S. Inenaga, Zs. Lipták, N. Prezza, M. Sciortino, and A. Toffanello 2021. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 .
  15. Novel results on the number of runs of the Burrows-Wheeler-Transform. In SOFSEM, Volume 12607 of LNCS, pp.  249–262. Springer. Giuliani et al. [2023] Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Giuliani, S., S. Inenaga, Zs. Lipták, G. Romana, M. Sciortino, and C. Urbina 2023. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 .
  16. Bit catastrophes for the Burrows-Wheeler Transform. In F. Drewes and M. Volkov (Eds.), Developments in Language Theory (DLT 2021), Cham, pp.  86–99. Springer Nature Switzerland. Kempa and Kociumaka [2022] Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Kempa, D. and T. Kociumaka. 2022. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 .
  17. Resolution of the Burrows-Wheeler Transform conjecture. Commun. ACM 65(6): 91–98 . Knuth et al. [1977] Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Knuth, D.E., J.H. Morris, and V.R. Pratt. 1977. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 .
  18. Fast pattern matching in strings. SIAM J. Comput. 6(2): 323–350 . Kociumaka et al. [2020] Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Kociumaka, T., G. Navarro, and N. Prezza 2020. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 .
  19. Towards a definitive measure of repetitiveness. In LATIN, Volume 12118 of Lect. Notes Comput. Sci., pp.  207–219. Springer. Lagarde and Perifel [2018] Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lagarde, G. and S. Perifel 2018. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 .
  20. Lempel-Ziv: a “one-bit catastrophe” but not a tragedy. In SODA, pp.  1478–1495. SIAM. Lam et al. [2009] Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lam, T.W., R. Li, A. Tam, S. Wong, E. Wu, and S.M. Yiu 2009. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 .
  21. High Throughput Short Read Alignment via Bi-directional BWT. In BIBM, pp.  31–36. IEEE Computer Society. Langmead et al. [2009] Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Langmead, B., C. Trapnell, M. Pop, and S.L. Salzberg. 2009. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 .
  22. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology 10(3): R25 . Li and Durbin [2010] Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Li, H. and R. Durbin. 2010. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 .
  23. Fast and accurate long-read alignment with Burrows–Wheeler transform. Bioinformatics 26(5): 589–595 . Lothaire [2002] Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 .
  24. Lothaire, M. 2002. Algebraic Combinatorics on Words. Cambridge Univ. Press. Mäkinen and Navarro [2005] Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mäkinen, V. and G. Navarro 2005. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 .
  25. Succinct suffix arrays based on run-length encoding. In CPM, Volume 3537 of Lecture Notes in Comp. Sc., pp.  45–56. Springer. Mantaci et al. [2017] Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mantaci, S., A. Restivo, G. Rosone, M. Sciortino, and L. Versari. 2017. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 .
  26. Measuring the clustering effect of BWT via RLE. Theoret. Comput. Sci. 698: 79 – 87 . Mantaci et al. [2003] Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Mantaci, S., A. Restivo, and M. Sciortino. 2003. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 .
  27. Burrows–Wheeler transform and Sturmian words. Information Processing Letters 86(5): 241–246 . Navarro [2022] Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 .
  28. Navarro, G. 2022. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Comput. Surv. 54(2): 29:1–29:31 . Rosone and Sciortino [2013] Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Rosone, G. and M. Sciortino 2013. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 .
  29. The Burrows-Wheeler transform between data compression and combinatorics on words. In 9th Conference on Computability in Europe (CiE 2013), pp.  353–364. Sciortino and Zamboni [2007] Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 .
  30. Sciortino, M. and L.Q. Zamboni 2007. Suffix automata and standard Sturmian words. In Developments in Language Theory (DLT 2007), Volume 4588 of Lect. Notes Comput. Sc., pp.  382–398. Springer. Seward [1996] Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 .
  31. Seward, J. 1996. https://sourceware.org/bzip2/manual/manual.html. Ziv and Lempel [1977] Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1977. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 .
  32. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3): 337–343 . Ziv and Lempel [1978] Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 . Ziv, J. and A. Lempel. 1978. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 .
  33. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5): 530–536 .
Citations (5)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now
X Twitter Logo Streamline Icon: https://streamlinehq.com

Tweets