License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
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DOI: 10.4230/LIPIcs.STACS.2023.11
URN: urn:nbn:de:0030-drops-176636
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/17663/
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Bergougnoux, Benjamin ; Korhonen, Tuukka ; Nederlof, Jesper

Tight Lower Bounds for Problems Parameterized by Rank-Width

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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.

BibTeX - Entry

@InProceedings{bergougnoux_et_al:LIPIcs.STACS.2023.11,
  author =	{Bergougnoux, Benjamin and Korhonen, Tuukka and Nederlof, Jesper},
  title =	{{Tight Lower Bounds for Problems Parameterized by Rank-Width}},
  booktitle =	{40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)},
  pages =	{11:1--11:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-266-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{254},
  editor =	{Berenbrink, Petra and Bouyer, Patricia and Dawar, Anuj and Kant\'{e}, Mamadou Moustapha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/17663},
  URN =		{urn:nbn:de:0030-drops-176636},
  doi =		{10.4230/LIPIcs.STACS.2023.11},
  annote =	{Keywords: rank-width, exponential time hypothesis, Boolean-width, parameterized algorithms, independent set, dominating set, maximum induced matching, feedback vertex set}
}

Keywords: rank-width, exponential time hypothesis, Boolean-width, parameterized algorithms, independent set, dominating set, maximum induced matching, feedback vertex set
Collection: 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)
Issue Date: 2023
Date of publication: 03.03.2023

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