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DOI: 10.4230/LIPIcs.FSTTCS.2012.236
URN: urn:nbn:de:0030-drops-38627
URL: http://drops.dagstuhl.de/opus/volltexte/2012/3862/
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Chakaravarthy, Venkatesan T. ; Modani, Natwar ; Natarajan, Sivaramakrishnan R. ; Roy, Sambuddha ; Sabharwal, Yogish

Density Functions subject to a Co-Matroid Constraint

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Abstract

In this paper we consider the problem of finding the densest subset subject to co-matroid constraints. We are given a monotone supermodular set function f defined over a universe U, and the density of a subset S is defined to be f(S)/|S|. This generalizes the concept of graph density. Co-matroid constraints are the following: given matroid M a set S is feasible, iff the complement of S is independent in the matroid. Under such constraints, the problem becomes NP-hard. The specific case of graph density has been considered in literature under specific co-matroid constraints, for example, the cardinality matroid and the partition matroid. We show a 2-approximation for finding the densest subset subject to co-matroid constraints. Thereby we improve the approximation guarantees for the result for partition matroids in the literature.

BibTeX - Entry

@InProceedings{chakaravarthy_et_al:LIPIcs:2012:3862,
  author =	{Venkatesan T. Chakaravarthy and Natwar Modani and Sivaramakrishnan R. Natarajan and Sambuddha Roy and Yogish Sabharwal},
  title =	{{Density Functions subject to a Co-Matroid Constraint}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012) },
  pages =	{236--248},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-47-7},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{18},
  editor =	{Deepak D'Souza and Telikepalli Kavitha and Jaikumar Radhakrishnan},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2012/3862},
  URN =		{urn:nbn:de:0030-drops-38627},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.FSTTCS.2012.236},
  annote =	{Keywords: Approximation Algorithms, Submodular Functions, Graph Density}
}

Keywords: Approximation Algorithms, Submodular Functions, Graph Density
Seminar: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)
Issue Date: 2012
Date of publication: 10.12.2012


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