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Density Functions subject to a Co-Matroid Constraint

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

Published 2012 in Foundations of Software Technology and Theoretical Computer Science

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.

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