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K-Shortest Simple Paths Using Biobjective Path Search (2309.10377v1)

Published 19 Sep 2023 in cs.DS and cs.DM

Abstract: In this paper we introduce a new algorithm for the \emph{$k$-Shortest Simple Paths} (\kspp{k}) problem with an asymptotic running time matching the state of the art from the literature. It is based on a black-box algorithm due to \citet{Roditty12} that solves at most $2k$ instances of the \emph{Second Shortest Simple Path} (\kspp{2}) problem without specifying how this is done. We fill this gap using a novel approach: we turn the scalar \kspp{2} into instances of the Biobjective Shortest Path problem. Our experiments on grid graphs and on road networks show that the new algorithm is very efficient in practice.

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References (30)
  1. Replacement Paths and k Simple Shortest Paths in Unweighted Directed Graphs. ACM Trans. Algorithms, 8(4), October 2012. ISSN 1549-6325. doi:10.1145/2344422.2344423.
  2. Computing the n best loopless paths in a network. Journal of the Society for Industrial and Applied Mathematics, 11(4):1096–1102, 1963. ISSN 03684245. URL http://www.jstor.org/stable/2946497.
  3. David Eppstein. k-Best Enumeration, pages 1003–1006. Springer New York, New York, NY, 2016. ISBN 978-1-4939-2864-4. doi:10.1007/978-1-4939-2864-4_733.
  4. M. Ehrgott. Multicriteria Optimization. Springer-Verlag, 2005. doi:10.1007/3-540-27659-9.
  5. E. L. Lawler. A procedure for computing the k best solutions to discrete optimization problems and its application to the shortest path problem. Management Science, 18(7):401–405, 1972. ISSN 00251909, 15265501. URL http://www.jstor.org/stable/2629357.
  6. J. Y. Yen. Finding the Lengths of All Shortest paths in N-Node Nonnegative-Distance Complete Networks Using 1/2121/21 / 2 N3 Additions and N3 Comparisons. Journal of the ACM (JACM), 19(3):423–424, 1972.
  7. E. W. Dijkstra. A note on two problems in connexion with graphs. Numerische Mathematik 1, 1(1):269–271, December 1959. doi:10.1007/bf01386390.
  8. Fibonacci heaps and their uses in improved network optimization algorithms. Journal of the ACM, 34(3):596–615, July 1987. doi:10.1145/28869.28874.
  9. A new implementation of Yen’s ranking loopless paths algorithm. Quarterly Journal of the Belgian, French and Italian Operations Research Societies, 1(2), June 2003. doi:10.1007/s10288-002-0010-2.
  10. A Sidetrack-Based Algorithm for Finding the k Shortest Simple Paths in a Directed Graph, 2016.
  11. David Eppstein. Finding the k Shortest Paths. SIAM Journal on Computing, 28(2):652–673, 1 1998. doi:10.1137/s0097539795290477.
  12. Gang Feng. Finding k shortest simple paths in directed graphs: A node classification algorithm. Networks, 64(1):6–17, 3 2014a. doi:10.1002/net.21552.
  13. Improved algorithms for the k simple shortest paths and the replacement paths problems. Information Processing Letters, 109(7):352–355, March 2009. doi:10.1016/j.ipl.2008.12.015.
  14. Seth Pettie. A new approach to all-pairs shortest paths on real-weighted graphs. Theoretical Computer Science, 312(1):47–74, 2004. ISSN 0304-3975. doi:10.1016/S0304-3975(03)00402-X. Automata, Languages and Programming.
  15. Directed Shortest Paths via Approximate Cost Balancing. J. ACM, 70(1), 12 2022. ISSN 0004-5411. doi:10.1145/3565019.
  16. Antonio Sedeño-Noda. Ranking One Million Simple Paths in Road Networks. Asia-Pacific Journal of Operational Research, 33(05):1650042, October 2016. doi:10.1142/s0217595916500421.
  17. Gang Feng. Improving Space Efficiency With Path Length Prediction for Finding k𝑘kitalic_k Shortest Simple Paths. IEEE Transactions on Computers, 63(10):2459–2472, 2014b. doi:10.1109/TC.2013.136.
  18. Deviation Algorithms For Ranking Shortest Paths. International Journal of Foundations of Computer Science, 10(03):247–261, September 1999. doi:10.1142/s0129054199000186.
  19. Replacement Paths and k Simple Shortest Paths in Unweighted Directed Graphs. In Luís Caires, Giuseppe F. Italiano, Luís Monteiro, Catuscia Palamidessi, and Moti Yung, editors, Automata, Languages and Programming, pages 249–260, Berlin, Heidelberg, 2005. Springer Berlin Heidelberg. ISBN 978-3-540-31691-6.
  20. Antonio Sedeño Noda and Marcos Colebrook. A Biobjective Dijkstra Algorithm. European Journal of Operational Research, 276(1):106–118, July 2019. doi:10.1016/j.ejor.2019.01.007.
  21. An FPTAS for Dynamic Multiobjective Shortest Path Problems. Algorithms, 14(2), 2021a. ISSN 1999-4893. doi:10.3390/a14020043.
  22. An Improved Multiobjective Shortest Path Algorithm. Computers and Operations Research, 135:105424, 2021b. ISSN 0305-0548. doi:10.1016/j.cor.2021.105424.
  23. Bi-Objective Search with Bi-Directional A*. In Petra Mutzel, Rasmus Pagh, and Grzegorz Herman, editors, 29th Annual European Symposium on Algorithms (ESA 2021), volume 204 of Leibniz International Proceedings in Informatics (LIPIcs), pages 3:1–3:15, Dagstuhl, Germany, 2021. Schloss Dagstuhl – Leibniz-Zentrum für Informatik. ISBN 978-3-95977-204-4. doi:10.4230/LIPIcs.ESA.2021.3.
  24. Targeted multiobjective Dijkstra algorithm. Networks, n/a(n/a), 2023. doi:10.1002/net.22174.
  25. Pierre Hansen. Bicriterion Path Problems. In Günter Fandel and Tomas Gal, editors, Multiple Criteria Decision Making Theory and Application, pages 109–127, Berlin, Heidelberg, 1980. Springer Berlin Heidelberg. ISBN 978-3-642-48782-8.
  26. Biobjective optimization problems on matroids with binary costs. Optimization, 72(7):1931–1960, 2023. doi:10.1080/02331934.2022.2044479.
  27. F. K. Bökler. Output-sensitive complexity of multiobjective combinatorial optimization with an application to the multiobjective shortest path problem. PhD thesis, Technische Universität Dortmund, 2018.
  28. Subcubic Equivalences Between Path, Matrix, and Triangle Problems. Journal of the ACM, 65(5):1–38, August 2018. doi:10.1145/3186893.
  29. 9th DIMACS Implementation Challenge - Shortest Paths. http://www.diag.uniroma1.it//~challenge9/, 2009. Accessed: 2021-12-15.
  30. Pedro Maristany de las Casas. maristanyPedro/kshortestpaths: Initial Release – Preprint Citation, September 2023. doi: 10.5281/zenodo.8324671.

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