2026-07-26T05:31:58Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:17663 2024-03-06T11:00:15Z ddc:004 open_access

Tight Lower Bounds for Problems Parameterized by Rank-Width Bergougnoux, Benjamin Korhonen, Tuukka Nederlof, Jesper rank-width exponential time hypothesis Boolean-width parameterized algorithms independent set dominating set maximum induced matching feedback vertex set 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Benjamin Bergougnoux and Tuukka Korhonen and Jesper Nederlof 2023 Is Part Of LIPIcs, Volume 254, 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.STACS.2023.11 urn:nbn:de:0030-drops-176636 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2023.11 eng https://creativecommons.org/licenses/by/4.0/legalcode