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URN: urn:nbn:de:0030-drops-23153
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Domination Problems in Nowhere-Dense Classes

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Abstract

We investigate the parameterized complexity of generalisations and variations of the dominating set problem on classes of graphs that are nowhere dense. In particular, we show that the distance-$d$ dominating-set problem, also known as the $(k,d)$-centres problem, is fixed-parameter tractable on any class that is nowhere dense and closed under induced subgraphs. This generalises known results about the dominating set problem on $H$-minor free classes, classes with locally excluded minors and classes of graphs of bounded expansion. A key feature of our proof is that it is based simply on the fact that these graph classes are uniformly quasi-wide, and does not rely on a structural decomposition. Our result also establishes that the distance-$d$ dominating-set problem is FPT on classes of bounded expansion, answering a question of Ne{\v s}et{\v r}il and Ossona de Mendez.

BibTeX - Entry

@InProceedings{dawar_et_al:LIPIcs:2009:2315,
  author =	{Anuj Dawar and Stephan Kreutzer},
  title =	{{Domination Problems in Nowhere-Dense Classes}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
  pages =	{157--168},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-13-2},
  ISSN =	{1868-8969},
  year =	{2009},
  volume =	{4},
  editor =	{Ravi Kannan and K. Narayan Kumar},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2009/2315},
  URN =		{urn:nbn:de:0030-drops-23153},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.FSTTCS.2009.2315},
  annote =	{Keywords: Dominating Set, distance-d dominating set, nowhere-dense graph classes, H-minor free graphs, fixed-parameter tractablility}
}

Keywords: Dominating Set, distance-d dominating set, nowhere-dense graph classes, H-minor free graphs, fixed-parameter tractablility
Seminar: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science
Issue date: 2009
Date of publication: 2009


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