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.2015.212
URN: urn:nbn:de:0030-drops-55846
URL: https://drops.dagstuhl.de/opus/volltexte/2015/5584/
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Jeong, Jisu ; Sæther, Sigve Hortemo ; Telle, Jan Arne

Maximum Matching Width: New Characterizations and a Fast Algorithm for Dominating Set

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Abstract

We give alternative definitions for maximum matching width, e.g., a graph G has mmw(G) <= k if and only if it is a subgraph of a chordal graph H and for every maximal clique X of H there exists A,B,C \subseteq X with A \cup B \cup C=X and |A|,|B|,|C| <= k such that any subset of X that is a minimal separator of H is a subset of either A, B or C. Treewidth and branchwidth have alternative definitions through intersections of subtrees, where treewidth focuses on nodes and branchwidth focuses on edges. We show that mm-width combines both aspects, focusing on nodes and on edges. Based on this we prove that given a graph G and a branch decomposition of mm-width k we can solve Dominating Set in time O^*(8^k), thereby beating O^*(3^{tw(G)}) whenever tw(G) > log_3(8) * k ~ 1.893 k. Note that mmw(G) <= tw(G)+1 <= 3 mmw(G) and these inequalities are tight. Given only the graph G and using the best known algorithms to find decompositions, maximum matching width will be better for solving Dominating Set whenever tw(G) > 1.549 * mmw(G).

BibTeX - Entry

@InProceedings{jeong_et_al:LIPIcs:2015:5584,
  author =	{Jisu Jeong and Sigve Hortemo Sæther and Jan Arne Telle},
  title =	{{Maximum Matching Width: New Characterizations and a Fast Algorithm for Dominating Set}},
  booktitle =	{10th International Symposium on Parameterized and Exact Computation (IPEC 2015)},
  pages =	{212--223},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-92-7},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{43},
  editor =	{Thore Husfeldt and Iyad Kanj},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2015/5584},
  URN =		{urn:nbn:de:0030-drops-55846},
  doi =		{10.4230/LIPIcs.IPEC.2015.212},
  annote =	{Keywords: FPT algorithms, treewidth, dominating set}
}

Keywords: FPT algorithms, treewidth, dominating set
Collection: 10th International Symposium on Parameterized and Exact Computation (IPEC 2015)
Issue Date: 2015
Date of publication: 19.11.2015


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