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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSTTCS.2009.2318
URN: urn:nbn:de:0030-drops-23186
URL: https://drops.dagstuhl.de/opus/volltexte/2009/2318/
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Fomin, Fedor V. ; Lokshtanov, Daniel ; Raman, Venkatesh ; Saurabh, Saket

Subexponential Algorithms for Partial Cover Problems

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09005.FominFedor.2318.pdf (0.2 MB)

Abstract

Partial Cover problems are optimization versions
of fundamental and well studied problems like {\sc Vertex Cover} and {\sc Dominating Set}.
Here one is interested in covering (or dominating) the maximum number of edges (or vertices) using a given number ($k$) of vertices, rather than covering all edges (or vertices). In general graphs, these problems are hard for parameterized complexity classes when parameterized by $k$.
It was recently shown by Amini et. al. [{\em FSTTCS 08}\,] that {\sc Partial Vertex Cover} and {\sc Partial Dominating Set} are fixed parameter tractable on large classes of sparse graphs, namely $H$-minor free graphs,
which include planar graphs and graphs of bounded genus. In particular, it was shown that on planar graphs both problems can be solved in time $2^{\cO(k)}n^{\cO(1)}$.

BibTeX - Entry

@InProceedings{fomin_et_al:LIPIcs:2009:2318,
  author =	{Fedor V. Fomin and Daniel Lokshtanov and Venkatesh Raman and Saket Saurabh},
  title =	{{Subexponential  Algorithms for Partial Cover Problems}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
  pages =	{193--201},
  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/2009/2318},
  URN =		{urn:nbn:de:0030-drops-23186},
  doi =		{10.4230/LIPIcs.FSTTCS.2009.2318},
  annote =	{Keywords: Partial cover problems, parameterized complexity, subexponential time algorithms, irrelevant vertex technique}
}

Keywords: Partial cover problems, parameterized complexity, subexponential time algorithms, irrelevant vertex technique
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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