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DOI: 10.4230/LIPIcs.IPEC.2018.19
URN: urn:nbn:de:0030-drops-102207
URL: https://drops.dagstuhl.de/opus/volltexte/2019/10220/
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Komusiewicz, Christian ; Kratsch, Dieter ; Le, Van Bang

Matching Cut: Kernelization, Single-Exponential Time FPT, and Exact Exponential Algorithms

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Abstract

In a graph, a matching cut is an edge cut that is a matching. Matching Cut, which is known to be NP-complete, is the problem of deciding whether or not a given graph G has a matching cut. In this paper we show that Matching Cut admits a quadratic-vertex kernel for the parameter distance to cluster and a linear-vertex kernel for the parameter distance to clique. We further provide an O^*(2^{dc(G)}) time and an O^*(2^{dc^-}(G)}) time FPT algorithm for Matching Cut, where dc(G) and dc^-(G) are the distance to cluster and distance to co-cluster, respectively. We also improve the running time of the best known branching algorithm to solve Matching Cut from O^*(1.4143^n) to O^*(1.3803^n). Moreover, we point out that, unless NP subseteq coNP/poly, Matching Cut does not admit a polynomial kernel when parameterized by treewidth.

BibTeX - Entry

@InProceedings{komusiewicz_et_al:LIPIcs:2019:10220,
  author =	{Christian Komusiewicz and Dieter Kratsch and Van Bang Le},
  title =	{{Matching Cut: Kernelization, Single-Exponential Time FPT, and Exact Exponential Algorithms}},
  booktitle =	{13th International Symposium on Parameterized and Exact  Computation (IPEC 2018)},
  pages =	{19:1--19:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-084-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{115},
  editor =	{Christophe Paul and Michal Pilipczuk},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10220},
  URN =		{urn:nbn:de:0030-drops-102207},
  doi =		{10.4230/LIPIcs.IPEC.2018.19},
  annote =	{Keywords: matching cut, decomposable graph, graph algorithm}
}

Keywords: matching cut, decomposable graph, graph algorithm
Seminar: 13th International Symposium on Parameterized and Exact Computation (IPEC 2018)
Issue Date: 2019
Date of publication: 25.01.2019


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