文章基本信息

标题：Subexponential-Time Algorithms for Finding Large Induced Sparse Subgraphs
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作者：Jana Novotn{'a ; Karolina Okrasa ; Michal Pilipczuk 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2019
卷号：148
页码：1-11
DOI：10.4230/LIPIcs.IPEC.2019.23
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：Let C and D be hereditary graph classes. Consider the following problem: given a graph G in D, find a largest, in terms of the number of vertices, induced subgraph of G that belongs to C. We prove that it can be solved in 2^{o(n)} time, where n is the number of vertices of G, if the following conditions are satisfied: - the graphs in C are sparse, i.e., they have linearly many edges in terms of the number of vertices; - the graphs in D admit balanced separators of size governed by their density, e.g., O(Delta) or O(sqrt{m}), where Delta and m denote the maximum degree and the number of edges, respectively; and - the considered problem admits a single-exponential fixed-parameter algorithm when parameterized by the treewidth of the input graph. This leads, for example, to the following corollaries for specific classes C and D: - a largest induced forest in a P_t-free graph can be found in 2^{O~(n^{2/3})} time, for every fixed t; and - a largest induced planar graph in a string graph can be found in 2^{O~(n^{3/4})} time.
关键词：subexponential algorithm; feedback vertex set; P_t-free graphs; string graphs