Scalable Hard Instances for Independent Set Reconfiguration

Authors Takehide Soh , Takumu Watanabe, Jun Kawahara , Akira Suzuki , Takehiro Ito



PDF
Thumbnail PDF

File

LIPIcs.SEA.2024.26.pdf
  • Filesize: 0.97 MB
  • 15 pages

Document Identifiers

Author Details

Takehide Soh
  • Information Infrastructure and Digital Transformation Initiatives Headquaters, Kobe University, Japan
Takumu Watanabe
  • Graduate School of Information Sciences, Tohoku University, Japan
Jun Kawahara
  • Graduate School of Informatics, Kyoto University, Japan
Akira Suzuki
  • Graduate School of Information Sciences, Tohoku University, Japan
Takehiro Ito
  • Graduate School of Information Sciences, Tohoku University, Japan

Cite As Get BibTex

Takehide Soh, Takumu Watanabe, Jun Kawahara, Akira Suzuki, and Takehiro Ito. Scalable Hard Instances for Independent Set Reconfiguration. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 26:1-26:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.SEA.2024.26

Abstract

The Token Jumping problem, also known as the independent set reconfiguration problem under the token jumping model, is defined as follows: Given a graph and two same-sized independent sets, determine whether one can be transformed into the other via a sequence of independent sets. Token Jumping has been extensively studied, mainly from the viewpoint of algorithmic theory, but its practical study has just begun. To develop a practically good solver, it is important to construct benchmark datasets that are scalable and hard. Here, "scalable" means the ability to change the scale of the instance while maintaining its characteristics by adjusting the given parameters; and "hard" means that the instance can become so difficult that it cannot be solved within a practical time frame by a solver. In this paper, we propose four types of instance series for Token Jumping. Our instance series is scalable in the sense that instance scales are controlled by the number of vertices. To establish their hardness, we focus on the numbers of transformation steps; our instance series requires exponential numbers of steps with respect to the number of vertices. Interestingly, three types of instance series are constructed by importing theories developed by algorithmic research. We experimentally evaluate the scalability and hardness of the proposed instance series, using the SAT solver and award-winning solvers of the international competition for Token Jumping.

Subject Classification

ACM Subject Classification
  • Computing methodologies → Discrete space search
Keywords
  • Combinatorial reconfiguration
  • Benckmark dataset
  • Graph Algorithm
  • PSPACE-complete

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads

References

  1. John Asplund, Kossi D. Edoh, Ruth Haas, Yulia Hristova, Beth Novick, and Brett Werner. Reconfiguration graphs of shortest paths. Discrete Mathematics, 341(10):2938-2948, 2018. URL: https://doi.org/10.1016/j.disc.2018.07.007.
  2. John Asplund and Brett Werner. Classification of reconfiguration graphs of shortest path graphs with no induced 4-cycles. Discrete Mathematics, 343(1):111640, 2020. URL: https://doi.org/10.1016/j.disc.2019.111640.
  3. Chitta Baral. Knowledge Representation, Reasoning and Declarative Problem Solving. Cambridge University Press, 2003. Google Scholar
  4. Armin Biere, Alessandro Cimatti, Edmund M. Clarke, and Yunshan Zhu. Symbolic model checking without BDDs. In International Conference on Tools and Algorithms for the Construction and Analysis of Systems, pages 193-207, 1999. Google Scholar
  5. Armin Biere, Katalin Fazekas, Mathias Fleury, and Maximillian Heisinger. CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling entering the SAT Competition 2020. In Tomas Balyo, Nils Froleyks, Marijn Heule, Markus Iser, Matti Järvisalo, and Martin Suda, editors, Proc. of SAT Competition 2020 - Solver and Benchmark Descriptions, volume B-2020-1 of Department of Computer Science Report Series B, pages 51-53. University of Helsinki, 2020. Google Scholar
  6. Paul Bonsma, Amer E. Mouawad, Naomi Nishimura, and Venkatesh Raman. The complexity of bounded length graph recoloring and CSP reconfiguration. In Parameterized and Exact Computation - 9th International Symposium, IPEC 2014, Wroclaw, Poland, September 10-12, 2014. Revised Selected Papers, pages 110-121, 2014. URL: https://doi.org/10.1007/978-3-319-13524-3_10.
  7. Paul S. Bonsma. The complexity of rerouting shortest paths. Theoretical Computer Science, 510:1-12, 2013. URL: https://doi.org/10.1016/j.tcs.2013.09.012.
  8. Paul S. Bonsma. Rerouting shortest paths in planar graphs. Discrete Applied Mathematics, 231:95-112, 2017. URL: https://doi.org/10.1016/j.dam.2016.05.024.
  9. Paul S. Bonsma and Luis Cereceda. Finding paths between graph colourings: PSPACE-completeness and superpolynomial distances. Theoretical Computer Science, 410(50):5215-5226, 2009. URL: https://doi.org/10.1016/j.tcs.2009.08.023.
  10. Nicolas Bousquet, Bastien Durain, Théo Pierron, and Stéphan Thomassé. Extremal independent set reconfiguration. Electronic Journal of Combinatorics, 30(3):P3.8, 2023. URL: https://doi.org/10.37236/11771.
  11. Nicolas Bousquet, Amer E. Mouawad, Naomi Nishimura, and Sebastian Siebertz. A survey on the parameterized complexity of the independent set and (connected) dominating set reconfiguration problems. CoRR, abs/2204.10526, 2022. URL: https://doi.org/10.48550/arXiv.2204.10526.
  12. Luis Cereceda, Jan van den Heuvel, and Matthew Johnson. Finding paths between 3-colorings. Journal of Graph Theory, 67(1):69-82, 2011. URL: https://doi.org/10.1002/jgt.20514.
  13. Remo Christen, Salomé Eriksson, Michael Katz, Christian Muise, Alice Petrov, Florian Pommerening, Jendrik Seipp, Silvan Sievers, and David Speck. PARIS: Planning algorithms for reconfiguring independent sets. In ICAPS 2023 Heuristics and Search for Domain-Independent Planning Workshop, 2023. URL: https://openreview.net/forum?id=LE8nB7aHV4.
  14. Niklas Eén and Niklas Sörensson. Temporal induction by incremental SAT solving. Electronic Notes in Theoretical Computer Science, 89(4), 2003. Google Scholar
  15. Kshitij Gajjar, Agastya Vibhuti Jha, Manish Kumar, and Abhiruk Lahiri. Reconfiguring shortest paths in graphs. In Proceedings of AAAI 2022, pages 9758-9766. AAAI Press, 2022. URL: https://ojs.aaai.org/index.php/AAAI/article/view/21211.
  16. Malik Ghallab, Dana S. Nau, and Paolo Traverso. Automated Planning - Theory and Practice. Elsevier, 2004. Google Scholar
  17. Parikshit Gopalan, Phokion G. Kolaitis, Elitza N. Maneva, and Christos H. Papadimitriou. The connectivity of Boolean satisfiability: Computational and structural dichotomies. SIAM Journal on Computing, 38(6):2330-2355, 2009. URL: https://doi.org/10.1137/07070440X.
  18. Aric A. Hagberg, Daniel A. Schult, and Pieter J. Swart. Exploring network structure, dynamics, and function using NetworkX. In Gaël Varoquaux, Travis Vaught, and Jarrod Millman, editors, Proceedings of the 7th Python in Science Conference, pages 11 - 15, Pasadena, CA USA, 2008. Google Scholar
  19. Tatsuhiko Hatanaka, Takehiro Ito, and Xiao Zhou. The list coloring reconfiguration problem for bounded pathwidth graphs. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, E98.A(6):1168-1178, 2015. URL: https://doi.org/10.1587/transfun.E98.A.1168.
  20. Tatsuhiko Hatanaka, Takehiro Ito, and Xiao Zhou. Parameterized complexity of the list coloring reconfiguration problem with graph parameters. Theoretical Computer Science, 739:65-79, 2018. URL: https://doi.org/10.1016/j.tcs.2018.05.005.
  21. Jan van den Heuvel. The complexity of change. In Surveys in Combinatorics 2013, volume 409 of London Mathematical Society Lecture Note Series, pages 127-160. Cambridge University Press, 2013. URL: https://doi.org/10.1017/CBO9781139506748.005.
  22. Takehiro Ito, Erik D. Demaine, Nicholas J. A. Harvey, Christos H. Papadimitriou, Martha Sideri, Ryuhei Uehara, and Yushi Uno. On the complexity of reconfiguration problems. Theoretical Computer Science, 412(12-14):1054-1065, 2011. URL: https://doi.org/10.1016/j.tcs.2010.12.005.
  23. Takehiro Ito, Jun Kawahara, Yu Nakahata, Takehide Soh, Akira Suzuki, Junichi Teruyama, and Takahisa Toda. ZDD-based algorithmic framework for solving shortest reconfiguration problems. In Andre A. Cire, editor, Integration of Constraint Programming, Artificial Intelligence, and Operations Research, pages 167-183, Cham, 2023. Springer Nature Switzerland. Google Scholar
  24. Mark Jerrum. Counting, Sampling and Integrating: Algorithms and Complexity. Birkhäuser Verlag, Basel, 2003. Google Scholar
  25. David S. Johnson and Michael A. Trick. Cliques, Coloring, and Satisfiability: Second DIMACS Implementation Challenge, October 11-13, 1993, volume 26. American Mathematical Society, 1996. Google Scholar
  26. Matthew Johnson, Dieter Kratsch, Stefan Kratsch, Viresh Patel, and Daniël Paulusma. Finding shortest paths between graph colourings. Algorithmica, 75(2):295-321, 2016. URL: https://doi.org/10.1007/s00453-015-0009-7.
  27. Marcin Kamiński, Paul Medvedev, and Martin Milanič. Shortest paths between shortest paths. Theoretical Computer Science, 412(39):5205-5210, 2011. URL: https://doi.org/10.1016/j.tcs.2011.05.021.
  28. Marcin Kamiński, Paul Medvedev, and Martin Milanič. Complexity of independent set reconfigurability problems. Theoretical Computer Science, 439:9-15, 2012. URL: https://doi.org/10.1016/j.tcs.2012.03.004.
  29. Richard E. Korf. Iterative-deepening-A*: An optimal admissible tree search. In Aravind K. Joshi, editor, Proceedings of the 9th International Joint Conference on Artificial Intelligence. Los Angeles, CA, USA, August 1985, pages 1034-1036. Morgan Kaufmann, 1985. Google Scholar
  30. Kazuhisa Makino, Suguru Tamaki, and Masaki Yamamoto. On the Boolean connectivity problem for Horn relations. Discrete Applied Mathematics, 158(18):2024-2030, 2010. URL: https://doi.org/10.1016/j.dam.2010.08.019.
  31. Kazuhisa Makino, Suguru Tamaki, and Masaki Yamamoto. An exact algorithm for the Boolean connectivity problem for k-CNF. Theoretical Computer Science, 412(35):4613-4618, 2011. URL: https://doi.org/10.1016/j.tcs.2011.04.041.
  32. Shin-ichi Minato. Zero-suppressed BDDs for set manipulation in combinatorial problems. In Proc. of the 30th ACM/IEEE design automation conference, pages 272-277, 1993. URL: https://doi.org/10.1145/157485.164890.
  33. Cristopher Moore and Stephan Mertens. The Nature of Computation. Oxford University Press, Inc., New York, 2011. Google Scholar
  34. Amer E. Mouawad, Naomi Nishimura, Vinayak Pathak, and Venkatesh Raman. Shortest reconfiguration paths in the solution space of Boolean formulas. SIAM Journal on Discrete Mathematics, 31(3):2185-2200, 2017. URL: https://doi.org/10.1137/16M1065288.
  35. Amer E. Mouawad, Naomi Nishimura, Venkatesh Raman, Narges Simjour, and Akira Suzuki. On the parameterized complexity of reconfiguration problems. Algorithmica, 78(1):274-297, 2017. URL: https://doi.org/10.1007/s00453-016-0159-2, URL: https://doi.org/10.1007/S00453-016-0159-2.
  36. Artur Niewiadomski, Piotr Switalski, Teofil Sidoruk, and Wojciech Penczek. Applying modern SAT-solvers to solving hard problems. Fundamenta Informaticae, 165(3-4):321-344, 2019. URL: https://doi.org/10.3233/FI-2019-1788.
  37. Naomi Nishimura. Introduction to reconfiguration. Algorithms, 11(4):Paper id 52, 2018. URL: https://doi.org/10.3390/a11040052.
  38. Carsten Sinz. Towards an optimal CNF encoding of boolean cardinality constraints. In Peter van Beek, editor, Principles and Practice of Constraint Programming - CP 2005, 11th International Conference, CP 2005, Sitges, Spain, October 1-5, 2005, Proceedings, volume 3709 of Lecture Notes in Computer Science, pages 827-831. Springer, 2005. URL: https://doi.org/10.1007/11564751_73.
  39. Takehide Soh, Yoshio Okamoto, and Takehiro Ito. Core challenge 2022: Solver and graph descriptions. CoRR, abs/2208.02495, 2022. https://arxiv.org/abs/2208.02495, URL: https://doi.org/10.48550/arXiv.2208.02495.
  40. Volker Turau and Christoph Weyer. Finding shortest reconfigurations sequences of independent sets. In Core Challenge 2022: Solver and Graph Descriptions, pages 3-14, 2022. Google Scholar
  41. Marcin Wrochna. Reconfiguration in bounded bandwidth and tree-depth. Journal of Computer and System Sciences, 93:1-10, 2018. URL: https://doi.org/10.1016/j.jcss.2017.11.003.
  42. Yuya Yamada, Mutsunori Banbara, Katsumi Inoue, Torsten Schaub, and Ryuhei Uehara. Combinatorial reconfiguration with answer set programming: Algorithms, encodings, and empirical analysis. In Ryuhei Uehara, Katsuhisa Yamanaka, and Hsu-Chun Yen, editors, WALCOM: Algorithms and Computation - 18th International Conference and Workshops on Algorithms and Computation, WALCOM 2024, Kanazawa, Japan, March 18-20, 2024, Proceedings, volume 14549 of Lecture Notes in Computer Science, pages 242-256. Springer, 2024. URL: https://doi.org/10.1007/978-981-97-0566-5_18.
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail