Pitch, extension complexity, and covering problems

Abstract

We study inequalities with bounded pitch. We first give a polynomial-time algorithm for approximately separating inequalities of bounded pitch for minimum knapsack polytopes, by showing how (not) to extend a similar result for inequalities with bounded coefficients. For general 0∕1 covering problems, we give a lower bound on the extension complexity of linear relaxations whose feasible points satisfy all inequalities of bounded pitch.