文章基本信息

标题：Close Relatives of Feedback Vertex Set Without Single-Exponential Algorithms Parameterized by Treewidth
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作者：Benjamin Bergougnoux ; Édouard Bonnet ; Nick Brettell 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2020
卷号：180
页码：1-17
DOI：10.4230/LIPIcs.IPEC.2020.3
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：The Cut & Count technique and the rank-based approach have lead to single-exponential FPT algorithms parameterized by treewidth, that is, running in time 2^ð'ª(tw)n^ð'ª(1), for Feedback Vertex Set and connected versions of the classical graph problems (such as Vertex Cover and Dominating Set). We show that Subset Feedback Vertex Set, Subset Odd Cycle Transversal, Restricted Edge-Subset Feedback Edge Set, Node Multiway Cut, and Multiway Cut are unlikely to have such running times. More precisely, we match algorithms running in time 2^ð'ª(tw log tw)n^ð'ª(1) with tight lower bounds under the Exponential Time Hypothesis, ruling out 2^o(tw log tw)n^ð'ª(1), where n is the number of vertices and tw is the treewidth of the input graph. Our algorithms extend to the weighted case, while our lower bounds also hold for the larger parameter pathwidth and do not require weights. We also show that, in contrast to Odd Cycle Transversal, there is no 2^o(tw log tw)n^ð'ª(1)-time algorithm for Even Cycle Transversal.
关键词：Subset Feedback Vertex Set; Multiway Cut; Parameterized Algorithms; Treewidth; Graph Modification; Vertex Deletion Problems