Document Open Access Logo

Kernelization Complexity of Solution Discovery Problems

Authors Mario Grobler , Stephanie Maaz , Amer E. Mouawad , Naomi Nishimura , Vijayaragunathan Ramamoorthi , Sebastian Siebertz

PDF

File

Thumbnail PDF
PDF
LIPIcs.ISAAC.2024.36.pdf
  • Filesize: 0.88 MB
  • 17 pages

Document Identifiers

Related Versions

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph algorithms
  • Theory of computation → Fixed parameter tractability
  • Mathematics of computing → Combinatorics
Keywords
  • solution discovery
  • kernelization
  • cut
  • independent set
  • vertex cover
  • dominating set

Metrics

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

Abstract

In the solution discovery variant of a vertex (edge) subset problem Π on graphs, we are given an initial configuration of tokens on the vertices (edges) of an input graph G together with a budget b. The question is whether we can transform this configuration into a feasible solution of Π on G with at most b modification steps. We consider the token sliding variant of the solution discovery framework, where each modification step consists of sliding a token to an adjacent vertex (edge). The framework of solution discovery was recently introduced by Fellows et al. [ECAI 2023] and for many solution discovery problems the classical as well as the parameterized complexity has been established. In this work, we study the kernelization complexity of the solution discovery variants of Vertex Cover, Independent Set, Dominating Set, Shortest Path, Matching, and Vertex Cut with respect to the parameters number of tokens k, discovery budget b, as well as structural parameters such as pathwidth.

Cite As Get BibTex

Mario Grobler, Stephanie Maaz, Amer E. Mouawad, Naomi Nishimura, Vijayaragunathan Ramamoorthi, and Sebastian Siebertz. Kernelization Complexity of Solution Discovery Problems. In 35th International Symposium on Algorithms and Computation (ISAAC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 322, pp. 36:1-36:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.ISAAC.2024.36

Author Details

Mario Grobler
  • University of Bremen, Germany
Stephanie Maaz
  • University of Waterloo, Canada
Amer E. Mouawad
  • American University of Beirut, Lebanon
Naomi Nishimura
  • University of Waterloo, Canada
Vijayaragunathan Ramamoorthi
  • University of Bremen, Germany
Sebastian Siebertz
  • University of Bremen, Germany

Funding

Naomi Nishimura, Stephanie Maaz: Research supported by the Natural Sciences and Engineering Research Council of Canada.
  • Ramamoorthi, Vijayaragunathan: Funded by the "Mind, Media, Machines" high-profile area at the University of Bremen.

References

  1. Hans L. Bodlaender, Gunther Cornelissen, and Marieke van der Wegen. Problems hard for treewidth but easy for stable gonality. Computing Research Repository (CoRR), abs/2202.06838, 2022. URL: https://arxiv.org/abs/2202.06838.
  2. Hans L. Bodlaender, Rodney G. Downey, Michael R. Fellows, and Danny Hermelin. On problems without polynomial kernels. Journal of Computer and System Sciences (J. Comput. Syst. Sci.), 75(8):423-434, 2009. URL: https://doi.org/10.1016/J.JCSS.2009.04.001.
  3. Hans L. Bodlaender, Bart M. P. Jansen, and Stefan Kratsch. Kernelization lower bounds by cross-composition. SIAM Journal on Discrete Mathematics (SIAM J. Discret. Math.), 28(1):277-305, 2014. URL: https://doi.org/10.1137/120880240.
  4. 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. Computing Research Repository (CoRR), abs/2204.10526, 2022. URL: https://doi.org/10.48550/arXiv.2204.10526.
  5. Liming Cai, Jianer Chen, Rodney G. Downey, and Michael R. Fellows. Advice classes of parameterized tractability. Annals of Pure and Applied Logic (Ann. Pure Appl. Log.), 84(1):119-138, 1997. URL: https://doi.org/10.1016/S0168-0072(95)00020-8.
  6. Marek Cygan, Fedor V. Fomin, Lukasz Kowalik, Daniel Lokshtanov, Dániel Marx, Marcin Pilipczuk, Michal Pilipczuk, and Saket Saurabh. Parameterized Algorithms. Springer, 2015. URL: https://doi.org/10.1007/978-3-319-21275-3.
  7. Reinhard Diestel. Graph Theory, 4th Edition, volume 173 of Graduate texts in mathematics. Springer, 2012. Google Scholar
  8. Rodney G. Downey and Michael R. Fellows. Parameterized Complexity. Monographs in Computer Science. Springer, 1999. URL: https://doi.org/10.1007/978-1-4612-0515-9.
  9. Rodney G. Downey and Michael R. Fellows. Fundamentals of Parameterized Complexity. Texts in Computer Science. Springer, 2013. URL: https://doi.org/10.1007/978-1-4471-5559-1.
  10. Paul Erdös and Richard Rado. Intersection theorems for systems of sets. Journal of the London Mathematical Society (J. Lond. Math.), s1-35(1):85-90, 1960. URL: https://doi.org/10.1112/jlms/s1-35.1.85.
  11. Michael R. Fellows, Mario Grobler, Nicole Megow, Amer E. Mouawad, Vijayaragunathan Ramamoorthi, Frances A. Rosamond, Daniel Schmand, and Sebastian Siebertz. On solution discovery via reconfiguration. In Kobi Gal, Ann Nowé, Grzegorz J. Nalepa, Roy Fairstein, and Roxana Radulescu, editors, ECAI 2023 - 26th European Conference on Artificial Intelligence, September 30 - October 4, 2023, Kraków, Poland - Including 12th Conference on Prestigious Applications of Intelligent Systems (PAIS 2023), volume 372 of Frontiers in Artificial Intelligence and Applications, pages 700-707. IOS Press, 2023. URL: https://doi.org/10.3233/FAIA230334.
  12. Lance Fortnow and Rahul Santhanam. Infeasibility of instance compression and succinct pcps for NP. Journal of Computer and System Sciences (J. Comput. Syst. Sci.), 77(1):91-106, 2011. URL: https://doi.org/10.1016/J.JCSS.2010.06.007.
  13. Mario Grobler, Stephanie Maaz, Nicole Megow, Amer E. Mouawad, Vijayaragunathan Ramamoorthi, Daniel Schmand, and Sebastian Siebertz. Solution discovery via reconfiguration for problems in P. In Karl Bringmann, Martin Grohe, Gabriele Puppis, and Ola Svensson, editors, 51st International Colloquium on Automata, Languages, and Programming, ICALP 2024, July 8-12, 2024, Tallinn, Estonia, volume 297 of LIPIcs, pages 76:1-76:20. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. URL: https://doi.org/10.4230/LIPICS.ICALP.2024.76.
  14. Stephan Kreutzer, Roman Rabinovich, and Sebastian Siebertz. Polynomial kernels and wideness properties of nowhere dense graph classes. ACM Transactions on Algorithms (ACM Trans. Algorithms), 15(2):24:1-24:19, 2019. URL: https://doi.org/10.1145/3274652.
  15. Van Bang Le and Florian Pfender. Complexity results for rainbow matchings. Theoretical Computer Science (Theor. Comput. Sci.), 524:27-33, 2014. URL: https://doi.org/10.1016/J.TCS.2013.12.013.
  16. Naomi Nishimura. Introduction to reconfiguration. Algorithms, 11(4):52, 2018. URL: https://doi.org/10.3390/A11040052.
  17. Michal Pilipczuk, Sebastian Siebertz, and Szymon Torunczyk. On the number of types in sparse graphs. In Anuj Dawar and Erich Grädel, editors, Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2018, Oxford, UK, July 09-12, 2018, pages 799-808. ACM, 2018. URL: https://doi.org/10.1145/3209108.3209178.
  18. Chee-Keng Yap. Some consequences of non-uniform conditions on uniform classes. Theoretical Computer Science (Theor. Comput. Sci.), 26:287-300, 1983. URL: https://doi.org/10.1016/0304-3975(83)90020-8.
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
© 2023-2025 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact