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.2018.6
URN: urn:nbn:de:0030-drops-102074
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/10207/
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Jaffke, Lars ; Kwon, O-joung ; Strømme, Torstein J. F. ; Telle, Jan Arne

Generalized Distance Domination Problems and Their Complexity on Graphs of Bounded mim-width

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LIPIcs-IPEC-2018-6.pdf (0.6 MB)

Abstract

We generalize the family of (sigma, rho)-problems and locally checkable vertex partition problems to their distance versions, which naturally captures well-known problems such as distance-r dominating set and distance-r independent set. We show that these distance problems are XP parameterized by the structural parameter mim-width, and hence polynomial on graph classes where mim-width is bounded and quickly computable, such as k-trapezoid graphs, Dilworth k-graphs, (circular) permutation graphs, interval graphs and their complements, convex graphs and their complements, k-polygon graphs, circular arc graphs, complements of d-degenerate graphs, and H-graphs if given an H-representation. To supplement these findings, we show that many classes of (distance) (sigma, rho)-problems are W[1]-hard parameterized by mim-width + solution size.

BibTeX - Entry

@InProceedings{jaffke_et_al:LIPIcs:2019:10207,
  author =	{Lars Jaffke and O-joung Kwon and Torstein J. F. Str{\o}mme and Jan Arne Telle},
  title =	{{Generalized Distance Domination Problems and Their Complexity on Graphs of Bounded mim-width}},
  booktitle =	{13th International Symposium on Parameterized and Exact  Computation (IPEC 2018)},
  pages =	{6:1--6:14},
  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/2019/10207},
  URN =		{urn:nbn:de:0030-drops-102074},
  doi =		{10.4230/LIPIcs.IPEC.2018.6},
  annote =	{Keywords: Graph Width Parameters, Graph Classes, Distance Domination Problems, Parameterized Complexity}
}

Keywords: Graph Width Parameters, Graph Classes, Distance Domination Problems, Parameterized Complexity
Collection: 13th International Symposium on Parameterized and Exact Computation (IPEC 2018)
Issue Date: 2019
Date of publication: 05.02.2019

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