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Documents authored by Natarajan, Sivaramakrishnan R.

Document
DOI: 10.4230/LIPIcs.FSTTCS.2013.275
Knapsack Cover Subject to a Matroid Constraint

Authors: Venkatesan T. Chakaravarthy, Anamitra Roy Choudhury, Sivaramakrishnan R. Natarajan, and Sambuddha Roy

Published in: LIPIcs, Volume 24, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013)

Abstract
We consider the Knapsack Covering problem subject to a matroid constraint. In this problem, we are given an universe U of n items where item i has attributes: a cost c(i) and a size s(i). We also have a demand D. We are also given a matroid M = (U, I) on the set U. A feasible solution S to the problem is one such that (i) the cumulative size of the items chosen is at least D, and (ii) the set S is independent in the matroid M (i.e. S is in I). The objective is to minimize the total cost of the items selected, sum_{i in S}c(i). Our main result proves a 2-factor approximation for this problem. The problem described above falls in the realm of mixed packing covering problems. We also consider packing extensions of certain other covering problems and prove that in such cases it is not possible to derive any constant factor pproximations.
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Venkatesan T. Chakaravarthy, Anamitra Roy Choudhury, Sivaramakrishnan R. Natarajan, and Sambuddha Roy. Knapsack Cover Subject to a Matroid Constraint. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 24, pp. 275-286, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@InProceedings{chakaravarthy_et_al:LIPIcs.FSTTCS.2013.275,
  author =	{Chakaravarthy, Venkatesan T. and Choudhury, Anamitra Roy and Natarajan, Sivaramakrishnan R. and Roy, Sambuddha},
  title =	{{Knapsack Cover Subject to a Matroid Constraint}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013)},
  pages =	{275--286},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-64-4},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{24},
  editor =	{Seth, Anil and Vishnoi, Nisheeth K.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2013.275},
  URN =		{urn:nbn:de:0030-drops-43795},
  doi =		{10.4230/LIPIcs.FSTTCS.2013.275},
  annote =	{Keywords: Approximation Algorithms, LP rounding, Matroid Constraints, Knapsack problems}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2012.236
Density Functions subject to a Co-Matroid Constraint

Authors: Venkatesan T. Chakaravarthy, Natwar Modani, Sivaramakrishnan R. Natarajan, Sambuddha Roy, and Yogish Sabharwal

Published in: LIPIcs, Volume 18, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)

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.
Cite as

Venkatesan T. Chakaravarthy, Natwar Modani, Sivaramakrishnan R. Natarajan, Sambuddha Roy, and Yogish Sabharwal. Density Functions subject to a Co-Matroid Constraint. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 18, pp. 236-248, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@InProceedings{chakaravarthy_et_al:LIPIcs.FSTTCS.2012.236,
  author =	{Chakaravarthy, Venkatesan T. and Modani, Natwar and Natarajan, Sivaramakrishnan R. and Roy, Sambuddha and Sabharwal, Yogish},
  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 =	{D'Souza, Deepak and Radhakrishnan, Jaikumar and Telikepalli, Kavitha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2012.236},
  URN =		{urn:nbn:de:0030-drops-38627},
  doi =		{10.4230/LIPIcs.FSTTCS.2012.236},
  annote =	{Keywords: Approximation Algorithms, Submodular Functions, Graph Density}
}
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