Parameterized Complexities of Dominating and Independent Set Reconfiguration

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

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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


We would like to thank the referees for useful comments.

Cite AsGet 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)


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.

Subject Classification

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


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