License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.IPEC.2019.23
URN: urn:nbn:de:0030-drops-114845
URL: https://drops.dagstuhl.de/opus/volltexte/2019/11484/
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Novotná, Jana ; Okrasa, Karolina ; Pilipczuk, Michal ; Rzazewski, Pawel ; van Leeuwen, Erik Jan ; Walczak, Bartosz

Subexponential-Time Algorithms for Finding Large Induced Sparse Subgraphs

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LIPIcs-IPEC-2019-23.pdf (0.7 MB)

Abstract

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.

BibTeX - Entry

@InProceedings{novotn_et_al:LIPIcs:2019:11484,
  author =	{Jana Novotn{\'a} and Karolina Okrasa and Michal Pilipczuk and Pawel Rzazewski and Erik Jan van Leeuwen and Bartosz Walczak},
  title =	{{Subexponential-Time Algorithms for Finding Large Induced Sparse Subgraphs}},
  booktitle =	{14th International Symposium on Parameterized and Exact Computation (IPEC 2019)},
  pages =	{23:1--23:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-129-0},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{148},
  editor =	{Bart M. P. Jansen and Jan Arne Telle},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2019/11484},
  URN =		{urn:nbn:de:0030-drops-114845},
  doi =		{10.4230/LIPIcs.IPEC.2019.23},
  annote =	{Keywords: subexponential algorithm, feedback vertex set, P_t-free graphs, string graphs}
}

Keywords: subexponential algorithm, feedback vertex set, P_t-free graphs, string graphs
Collection: 14th International Symposium on Parameterized and Exact Computation (IPEC 2019)
Issue Date: 2019
Date of publication: 04.12.2019

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