License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2023.11
URN: urn:nbn:de:0030-drops-176636
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/17663/
Bergougnoux, Benjamin ;
Korhonen, Tuukka ;
Nederlof, Jesper
Tight Lower Bounds for Problems Parameterized by Rank-Width
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: |
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rank-width, exponential time hypothesis, Boolean-width, parameterized algorithms, independent set, dominating set, maximum induced matching, feedback vertex set |
Collection: |
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40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023) |
Issue Date: |
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2023 |
Date of publication: |
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03.03.2023 |