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DOI: 10.4230/LIPIcs.FSTTCS.2009.2315
URN: urn:nbn:de:0030-drops-23153
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2009/2315/
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Dawar, Anuj ; Kreutzer, Stephan

Domination Problems in Nowhere-Dense Classes

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09005.DawarAnuj.2315.pdf (0.2 MB)

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 =		{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
Collection: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science
Issue Date: 2009
Date of publication: 14.12.2009

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