Reconfiguring Independent Sets on Interval Graphs

Authors Marcin Briański, Stefan Felsner, Jędrzej Hodor, Piotr Micek



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Author Details

Marcin Briański
  • Theoretical Computer Science Department, Faculty of Mathematics and Computer Science, Jagiellonian University, Kraków, Poland
Stefan Felsner
  • Institut für Mathematik, Technische Universität Berlin, Germany
Jędrzej Hodor
  • Theoretical Computer Science Department, Faculty of Mathematics and Computer Science, Jagiellonian University, Kraków, Poland
Piotr Micek
  • Theoretical Computer Science Department, Faculty of Mathematics and Computer Science, Jagiellonian University, Kraków, Poland

Cite AsGet BibTex

Marcin Briański, Stefan Felsner, Jędrzej Hodor, and Piotr Micek. Reconfiguring Independent Sets on Interval Graphs. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 23:1-23:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.MFCS.2021.23

Abstract

We study reconfiguration of independent sets in interval graphs under the token sliding rule. We show that if two independent sets of size k are reconfigurable in an n-vertex interval graph, then there is a reconfiguration sequence of length 𝒪(k⋅ n²). We also provide a construction in which the shortest reconfiguration sequence is of length Ω(k²⋅ n). As a counterpart to these results, we also establish that Independent Set Reconfiguration is PSPACE-hard on incomparability graphs, of which interval graphs are a special case.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph theory
Keywords
  • reconfiguration
  • independent sets
  • interval graphs

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References

  1. Marthe Bonamy and Nicolas Bousquet. Token sliding on chordal graphs. In Graph-Theoretic Concepts in Computer Science, Proc. WG 2017, volume 10520 of LNCS, pages 127-139. Springer, 2017. Google Scholar
  2. Paul Bonsma, Marcin Kamiński, and Marcin Wrochna. Reconfiguring independent sets in claw-free graphs. In R. Ravi and Inge Li Gørtz, editors, Algorithm Theory, Proc. SWAT 2014, volume 8503 of LNCS, pages 86-97. Springer, 2014. Google Scholar
  3. Nicolas Bousquet. Talk at the graph theory seminar in Bordeaux, October 02, 2020. URL: https://webconf.u-bordeaux.fr/b/mar-ef4-zed.
  4. Erik D. Demaine, Martin L. Demaine, Eli Fox-Epstein, Duc A. Hoang, Takehiro Ito, Hirotaka Ono, Yota Otachi, Ryuhei Uehara, and Takeshi Yamada. Polynomial-time algorithm for sliding tokens on trees. In Hee-Kap Ahn and Chan-Su Shin, editors, Algorithms and Computation, Proc. ISAAC 2014, volume 8889 of LNCS, pages 389-400. Springer, 2014. Google Scholar
  5. Eli Fox-Epstein, Duc A Hoang, Yota Otachi, and Ryuhei Uehara. Sliding token on bipartite permutation graphs. In Algorithms and Computation, Proc. ISAAC 2015, volume 9472 of LNCS, pages 237-247. Springer, 2015. Google Scholar
  6. Robert A. Hearn and Erik D. Demaine. Pspace-completeness of sliding-block puzzles and other problems through the nondeterministic constraint logic model of computation. Theoretical Computer Science, 343(1):72-96, 2005. Google Scholar
  7. Marcin Kamiński, Paul Medvedev, and Martin Milanič. Complexity of independent set reconfigurability problems. Theoretical Computer Science, 439:9-15, 2012. Google Scholar
  8. Daniel Lokshtanov and Amer E. Mouawad. The complexity of independent set reconfiguration on bipartite graphs. ACM Trans. Algorithms, 15(1):19 pages, 2018. Article No.: 7. Google Scholar
  9. Naomi Nishimura. Introduction to reconfiguration. Algorithms, 11(4):52, 2018. Google Scholar
  10. Marcin Wrochna. Reconfiguration in bounded bandwidth and tree-depth. Journal of Computer and System Sciences, 93:1-10, 2018. Google Scholar
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