Approximate fixed-rank closures of covering problems

Consider a 0/1 integer program min{cT x : Ax b, x {0, 1}n } where A is nonnegative. We show that if the number of minimal covers of Ax b is polynomially bounded, then there is a polynomially large lift-and-project relaxation whose value is arbitrarily close to being at least as good as that given by the rank q cuts, for any fixed q. A special case of this result is that given by set-covering problems, or, generally, problems where the coefficients in A and b are bounded.

• Type: Journal
• Year: 2006
• Where: MP
• Authors: Daniel Bienstock, Mark Zuckerberg
• Keywords: Integer Program, Large Lift-and-project Relaxation, Minimal Covers, MP 2006