LIPIcs.FSTTCS.2012.236.pdf
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Density Functions subject to a Co-Matroid Constraint
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IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS) - License:
Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license
- Publication Date: 2012-12-14
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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)
https://doi.org/10.4230/LIPIcs.FSTTCS.2012.236
https://doi.org/10.4230/LIPIcs.FSTTCS.2012.236
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.
Keywords
- Approximation Algorithms
- Submodular Functions
- Graph Density
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