$$\ell _1$$-sparsity Approximation Bounds for Packing Integer Programs

Abstract

We consider approximation algorithms for packing integer programs (PIPs) of the form max{ c, x : Ax ≤ b, x ∈ {0, 1} n } where c, A, and b are nonnegative. We let W = mini,j bi/Ai,j denote the width of A which is at least 1. Previous work by Bansal et al. [1] obtained an Ω( 1 ∆ 1/⌊W ⌋ 0 1 1+∆ 1 /W ) 1/(W −1) )-approximation. We also obtain a (1 − ǫ)-approximation when W = Ω( log(∆ 1 /ǫ) ǫ 2 ).