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Tight Lower Bounds for Problems Parameterized by Rank-Width

Authors Benjamin Bergougnoux , Tuukka Korhonen , Jesper Nederlof

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Author Details

Benjamin Bergougnoux
  • University of Warsaw, Poland
Tuukka Korhonen
  • University of Bergen, Norway
Jesper Nederlof
  • Utrecht University, The Netherlands

Funding

  • Korhonen, Tuukka: Supported by the Research Council of Norway via the project BWCA (grant no. 314528).
  • Nederlof, Jesper: Supported by the project CRACKNP that has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 853234).

Acknowledgements

This work was initiated while the authors attended the “2022 Advances in Parameterized Graph Algorithms” workshop.

Cite AsGet BibTex

Benjamin Bergougnoux, Tuukka Korhonen, and Jesper Nederlof. Tight Lower Bounds for Problems Parameterized by Rank-Width. In 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 254, pp. 11:1-11:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.STACS.2023.11

Abstract

We show that there is no 2^o(k²) n^O(1) time algorithm for Independent Set on n-vertex graphs with rank-width k, unless the Exponential Time Hypothesis (ETH) fails. Our lower bound matches the 2^O(k²) n^O(1) time algorithm given by Bui-Xuan, Telle, and Vatshelle [Discret. Appl. Math., 2010] and it answers the open question of Bergougnoux and Kanté [SIAM J. Discret. Math., 2021]. We also show that the known 2^O(k²) n^O(1) time algorithms for Weighted Dominating Set, Maximum Induced Matching and Feedback Vertex Set parameterized by rank-width k are optimal assuming ETH. Our results are the first tight ETH lower bounds parameterized by rank-width that do not follow directly from lower bounds for n-vertex graphs.

Subject Classification

ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
Keywords
  • rank-width
  • exponential time hypothesis
  • Boolean-width
  • parameterized algorithms
  • independent set
  • dominating set
  • maximum induced matching
  • feedback vertex set

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