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.2019.13
URN: urn:nbn:de:0030-drops-114747
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/11474/
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Eto, Hiroshi ; Hanaka, Tesshu ; Kobayashi, Yasuaki ; Kobayashi, Yusuke

Parameterized Algorithms for Maximum Cut with Connectivity Constraints

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LIPIcs-IPEC-2019-13.pdf (0.6 MB)

Abstract

We study two variants of Maximum Cut, which we call Connected Maximum Cut and Maximum Minimal Cut, in this paper. In these problems, given an unweighted graph, the goal is to compute a maximum cut satisfying some connectivity requirements. Both problems are known to be NP-complete even on planar graphs whereas Maximum Cut on planar graphs is solvable in polynomial time. We first show that these problems are NP-complete even on planar bipartite graphs and split graphs. Then we give parameterized algorithms using graph parameters such as clique-width, tree-width, and twin-cover number. Finally, we obtain FPT algorithms with respect to the solution size.

BibTeX - Entry

@InProceedings{eto_et_al:LIPIcs:2019:11474,
  author =	{Hiroshi Eto and Tesshu Hanaka and Yasuaki Kobayashi and Yusuke Kobayashi},
  title =	{{Parameterized Algorithms for Maximum Cut with Connectivity Constraints}},
  booktitle =	{14th International Symposium on Parameterized and Exact Computation (IPEC 2019)},
  pages =	{13:1--13:15},
  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/2019/11474},
  URN =		{urn:nbn:de:0030-drops-114747},
  doi =		{10.4230/LIPIcs.IPEC.2019.13},
  annote =	{Keywords: Maximum cut, Parameterized algorithm, NP-hardness, Graph parameter}
}

Keywords: Maximum cut, Parameterized algorithm, NP-hardness, Graph parameter
Collection: 14th International Symposium on Parameterized and Exact Computation (IPEC 2019)
Issue Date: 2019
Date of publication: 04.12.2019

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