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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


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

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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)


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
  • rank-width
  • exponential time hypothesis
  • Boolean-width
  • parameterized algorithms
  • independent set
  • dominating set
  • maximum induced matching
  • feedback vertex set


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