On k-Column Sparse Packing Programs

Abstract

We consider the class of packing integer programs (PIPs) that are column sparse, i.e. there is a specified upper bound k on the number of constraints that each variable appears in. We give an (ek+o(k))-approximation algorithm for k-column sparse PIPs, improving on recent results of k2· 2k and O(k2). We also show that the integrality gap of our linear programming relaxation is at least 2k-1; it is known that k-column sparse PIPs are (k/ k)-hard to approximate. We also extend our result (at the loss of a small constant factor) to the more general case of maximizing a submodular objective over k-column sparse packing constraints.