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Parameterized Complexities of Dominating and Independent Set Reconfiguration

Authors Hans L. Bodlaender , Carla Groenland , Céline M. F. Swennenhuis

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ACM Subject Classification
  • Theory of computation → Problems, reductions and completeness
  • Theory of computation → Parameterized complexity and exact algorithms
Keywords
  • Parameterized complexity
  • independent set reconfiguration
  • dominating set reconfiguration
  • W-hierarchy
  • XL
  • XNL
  • XNLP

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Abstract

We settle the parameterized complexities of several variants of independent set reconfiguration and dominating set reconfiguration, parameterized by the number of tokens. We show that both problems are XL-complete when there is no limit on the number of moves and XNL-complete when a maximum length 𝓁 for the sequence is given in binary in the input. The problems are known to be XNLP-complete when 𝓁 is given in unary instead, and W[1]- and W[2]-hard respectively when 𝓁 is also a parameter. We complete the picture by showing membership in those classes. 
Moreover, we show that for all the variants that we consider, token sliding and token jumping are equivalent under pl-reductions. We introduce partitioned variants of token jumping and token sliding, and give pl-reductions between the four variants that have precise control over the number of tokens and the length of the reconfiguration sequence.

Cite As Get BibTex

Hans L. Bodlaender, Carla Groenland, and Céline M. F. Swennenhuis. Parameterized Complexities of Dominating and Independent Set Reconfiguration. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 9:1-9:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.IPEC.2021.9

Author Details

Hans L. Bodlaender
  • Department of Information and Computing Sciences, Utrecht University, The Netherlands
Carla Groenland
  • Department of Information and Computing Sciences, Utrecht University, The Netherlands
Céline M. F. Swennenhuis
  • Department of Mathematics and Computer Science, Eindhoven University of Technology, The Netherlands

Funding

  • Groenland, Carla: Supported by the project CRACKNP that has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research innovation programme (grant agreement No 853234).
  • Swennenhuis, Céline M. F.: Supported by the Netherlands Organization for Scientific Research under project no. 613.009.031b.

Acknowledgements

We would like to thank the referees for useful comments.

References

  1. Hans L. Bodlaender, Carla Groenland, Jesper Nederlof, and Céline M. F. Swennenhuis. Parameterized Problems Complete for Nondeterministic FPT time and Logarithmic Space. arXiv:2105.14882, 2021. Google Scholar
  2. Hans L. Bodlaender, Carla Groenland, and Céline M. F. Swennenhuis. Parameterized complexities of dominating and independent set reconfiguration. CoRR, abs/2106.15907, 2021. URL: http://arxiv.org/abs/2106.15907.
  3. Yijia Chen, Jörg Flum, and Martin Grohe. Bounded nondeterminism and alternation in parameterized complexity theory. In 18th Annual IEEE Conference on Computational Complexity (Complexity 2003), 7-10 July 2003, Aarhus, Denmark, pages 13-29. IEEE Computer Society, 2003. URL: https://doi.org/10.1109/CCC.2003.1214407.
  4. Rodney G. Downey and Michael R. Fellows. Parameterized Complexity. Springer, 1999. Google Scholar
  5. Michael Elberfeld, Christoph Stockhusen, and Till Tantau. On the space and circuit complexity of parameterized problems: Classes and completeness. Algorithmica, 71(3):661-701, 2015. URL: https://doi.org/10.1007/s00453-014-9944-y.
  6. 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):1054-1065, 2011. Google Scholar
  7. Takehiro Ito, Marcin Kamiński, Hirotaka Ono, Akira Suzuki, Ryuhei Uehara, and Katsuhisa Yamanaka. On the parameterized complexity for token jumping on graphs. In T. V. Gopal, Manindra Agrawal, Angsheng Li, and S. Barry Cooper, editors, Theory and Applications of Models of Computation, pages 341-351, Cham, 2014. Springer International Publishing. Google Scholar
  8. Takehiro Ito, Hirotaka Ono, and Yota Otachi. Reconfiguration of cliques in a graph. In Proceedings of the 12th Annual Conference on Theory and Applications of Models of Computation, pages 212-223, 2015. Google Scholar
  9. 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.
  10. Harry R. Lewis and Christos H. Papadimitriou. Symmetric space-bounded computation. Theoretical Computer Science, 19(2):161-187, 1982. Google Scholar
  11. Daniel Lokshtanov and Amer E. Mouawad. The complexity of independent set reconfiguration on bipartite graphs. ACM Trans. Algorithms, 15(1), 2018. Google Scholar
  12. 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.
  13. Naomi Nishimura. Introduction to reconfiguration. Algorithms, 11(4), 2018. Google Scholar
  14. Jan van den Heuvel. The complexity of change. Surveys in Combinatorics, 409:127-160, 2013. Google Scholar
  15. Michael Wehar. On the complexity of intersection non-emptiness problems. PhD thesis, State University of New York at Buffalo, 2017. Google Scholar
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