Papers
Topics
Authors
Recent
Detailed Answer
Quick Answer
Concise responses based on abstracts only
Detailed Answer
Well-researched responses based on abstracts and relevant paper content.
Custom Instructions Pro
Preferences or requirements that you'd like Emergent Mind to consider when generating responses
Gemini 2.5 Flash
Gemini 2.5 Flash 45 tok/s
Gemini 2.5 Pro 52 tok/s Pro
GPT-5 Medium 30 tok/s Pro
GPT-5 High 24 tok/s Pro
GPT-4o 96 tok/s Pro
Kimi K2 206 tok/s Pro
GPT OSS 120B 457 tok/s Pro
Claude Sonnet 4 36 tok/s Pro
2000 character limit reached

Non-adaptive Group Testing on Graphs (1511.09196v5)

Published 30 Nov 2015 in cs.DS and cs.LG

Abstract: Grebinski and Kucherov (1998) and Alon et al. (2004-2005) study the problem of learning a hidden graph for some especial cases, such as hamiltonian cycle, cliques, stars, and matchings. This problem is motivated by problems in chemical reactions, molecular biology and genome sequencing. In this paper, we present a generalization of this problem. Precisely, we consider a graph G and a subgraph H of G and we assume that G contains exactly one defective subgraph isomorphic to H. The goal is to find the defective subgraph by testing whether an induced subgraph contains an edge of the defective subgraph, with the minimum number of tests. We present an upper bound for the number of tests to find the defective subgraph by using the symmetric and high probability variation of Lov\'asz Local Lemma.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (23)
  1. M. Aigner. Search problems on graphs. Discrete Applied Mathematics, 14(3):215 – 230, 1986. ISSN 0166-218X. http://dx.doi.org/10.1016/0166-218X(86)90026-0. URL http://www.sciencedirect.com/science/article/pii/0166218X86900260.
  2. N. Alon and V. Asodi. Learning a hidden subgraph. SIAM Journal on Discrete Mathematics, 18(4):697–712, 2005.
  3. N. Alon and J. H. Spencer. The probabilistic method. Wiley-Interscience Series in Discrete Mathematics and Optimization. John Wiley & Sons Inc., Hoboken, NJ, third edition, 2008. ISBN 978-0-470-17020-5.
  4. Learning a hidden matching. SIAM Journal on Computing, 33(2):487–501, 2004.
  5. D. Angluin and J. Chen. Learning a hidden graph using queries per edge. Journal of Computer and System Sciences, 74(4):546 – 556, 2008. ISSN 0022-0000. http://dx.doi.org/10.1016/j.jcss.2007.06.006. URL http://www.sciencedirect.com/science/article/pii/S0022000007000724.
  6. An optimal procedure for gap closing in whole genome shotgun sequencing. In Proceedings of the Fifth Annual International Conference on Computational Biology, RECOMB ’01, pages 22–30, New York, NY, USA, 2001. ACM. ISBN 1-58113-353-7. 10.1145/369133.369152. URL http://doi.acm.org/10.1145/369133.369152.
  7. Combinatorial Search on Graphs Motivated by Bioinformatics Applications: A Brief Survey, pages 16–27. Springer Berlin Heidelberg, Berlin, Heidelberg, 2005. ISBN 978-3-540-31468-4. 10.1007/11604686_2. URL http://dx.doi.org/10.1007/11604686_2.
  8. Reconstruction of hidden graphs and threshold group testing. Journal of Combinatorial Optimization, 22(2):270–281, 2011. ISSN 1382-6905. 10.1007/s10878-010-9291-0. URL http://dx.doi.org/10.1007/s10878-010-9291-0.
  9. Learning a hidden graph. Optimization Letters, 8(8):2341–2348, Dec 2014. ISSN 1862-4480. 10.1007/s11590-014-0751-9. URL https://doi.org/10.1007/s11590-014-0751-9.
  10. The Lovász local lemma and its applications to some combinatorial arrays. Designs, Codes and Cryptography, 32(1-3):121–134, 2004. ISSN 0925-1022. 10.1023/B:DESI.0000029217.97956.26. URL http://dx.doi.org/10.1023/B%3ADESI.0000029217.97956.26.
  11. R. Dorfman. The detection of defective members of large populations. Ann. Math. Statist., 14(4):436–440, 12 1943. 10.1214/aoms/1177731363. URL http://dx.doi.org/10.1214/aoms/1177731363.
  12. D. Du and F. Hwang. Combinatorial Group Testing and Its Applications. Applied Mathematics. World Scientific, 2000. ISBN 9789810241070. URL http://books.google.com/books?id=KW5-CyUUOggC.
  13. D. Du and F. Hwang. Pooling Designs and Nonadaptive Group Testing: Important Tools for DNA Sequencing. Series on applied mathematics. World Scientific, 2006. ISBN 9789812568229. URL http://books.google.com/books?id=AJcoAQAAMAAJ.
  14. V. Grebinski and G. Kucherov. Reconstructing a hamiltonian cycle by querying the graph: Application to DNA physical mapping. Discrete Applied Mathematics, 88(1–3):147 – 165, 1998. ISSN 0166-218X. http://dx.doi.org/10.1016/S0166-218X(98)00070-5. URL http://www.sciencedirect.com/science/article/pii/S0166218X98000705.
  15. V. Grebinski and G. Kucherov. Optimal reconstruction of graphs under the additive model. Algorithmica, 28(1):104–124, 2000. ISSN 1432-0541. 10.1007/s004530010033. URL http://dx.doi.org/10.1007/s004530010033.
  16. J. J. Hein. An optimal algorithm to reconstruct trees from additive distance data. Bulletin of Mathematical Biology, 51(5):597–603, 1989. ISSN 1522-9602. 10.1007/BF02459968. URL http://dx.doi.org/10.1007/BF02459968.
  17. H.-B. C. F. K. Hwang. A survey on nonadaptive group testing algorithms through the angle of decoding. Journal of Combinatorial Optimization, 15, 01 2008. 10.1007/s10878-007-9083-3. URL http://libgen.org/scimag/index.php?s=10.1007/s10878-007-9083-3.
  18. On the complexity of distance-based evolutionary tree reconstruction. In Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA ’03, pages 444–453, Philadelphia, PA, USA, 2003. Society for Industrial and Applied Mathematics. ISBN 0-89871-538-5. URL http://dl.acm.org/citation.cfm?id=644108.644179.
  19. A group testing method for finding patterns in data. Discrete Applied Mathematics, 144(1–2):149 – 157, 2004. ISSN 0166-218X. http://dx.doi.org/10.1016/j.dam.2003.07.009. URL http://www.sciencedirect.com/science/article/pii/S0166218X04001933.
  20. A survey on combinatorial group testing algorithms with applications to DNA library screening. In Discrete mathematical problems with medical applications, volume 55 of DIMACS Ser. Discrete Math. Theoret. Comput. Sci., pages 171–182. Amer. Math. Soc., 2000.
  21. L. Reyzin and N. Srivastava. Algorithmic Learning Theory: 18th International Conference, ALT 2007, Sendai, Japan, October 1-4, 2007. Proceedings, chapter Learning and Verifying Graphs Using Queries with a Focus on Edge Counting, pages 285–297. Springer Berlin Heidelberg, Berlin, Heidelberg, 2007a. ISBN 978-3-540-75225-7. 10.1007/978-3-540-75225-7_24. URL http://dx.doi.org/10.1007/978-3-540-75225-7_24.
  22. L. Reyzin and N. Srivastava. On the longest path algorithm for reconstructing trees from distance matrices. Inf. Process. Lett., 101(3):98–100, Feb. 2007b. ISSN 0020-0190. 10.1016/j.ipl.2006.08.013. URL http://dx.doi.org/10.1016/j.ipl.2006.08.013.
  23. A new approach using multiplex long accurate pcr and yeast artificial chromosomes for bacterial chromosome mapping and sequencing. Genome Research, 6(5):448–453, 1996. 10.1101/gr.6.5.448. URL http://genome.cshlp.org/content/6/5/448.abstract.
Citations (1)
View on Semantic Scholar
List To Do Tasks Checklist Streamline Icon: https://streamlinehq.com

Collections

Sign up for free to add this paper to one or more collections.

User Circle Single Streamline Icon: https://streamlinehq.com Sign Up

Summary

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

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now
Dice Question Streamline Icon: https://streamlinehq.com

Follow-Up Questions

We haven't generated follow-up questions for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Generate Now

Authors (1)

  1. Hamid Kameli