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arXiv · 1207.5215

Density Functions subject to a Co-Matroid Constraint

Venkatesan T. Chakaravarthy·Natwar Modani·Sivaramakrishnan R. Natarajan·Sambuddha Roy·Yogish Sabharwal
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Abstract

In this paper we consider the problem of finding the {\em densest} subset subject to {\em co-matroid constraints}. We are given a {\em monotone supermodular} set function $f$ defined over a universe $U$, and the density of a subset $S$ is defined to be $f(S)/\crd{S}$. This generalizes the concept of graph density. Co-matroid constraints are the following: given matroid $\calM$ a set $S$ is feasible, iff the complement of $S$ is {\em 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. Thus, for instance, we improve the approximation guarantees for the result for partition matroids in the literature.

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Venkatesan T. Chakaravarthy, Natwar Modani, Sivaramakrishnan R. Natarajan, Sambuddha Roy, Yogish Sabharwal. 2012-07-30. Density Functions subject to a Co-Matroid Constraint. https://arxiv.org/abs/1207.5215

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