General Cut-Generating Procedures for the Stable Set Polytope

TL;DR

This paper introduces a general method for generating cuts for the stable set polytope, capable of producing both rank and non-rank inequalities, and demonstrates its effectiveness through computational experiments.

Contribution

It presents a novel, general separation procedure that extends existing methods by generating a broader class of valid inequalities for the stable set polytope.

Findings

Effective cut generation on DIMACS benchmark instances

Produces both rank and non-rank valid inequalities

Potentially improves optimization over the stable set polytope

Abstract

We propose general separation procedures for generating cuts for the stable set polytope, inspired by a procedure by Rossi and Smriglio and applying a lifting method by Xavier and Camp\^{e}lo. In contrast to existing cut-generating procedures, ours generate both rank and non-rank valid inequalities, hence they are of a more general nature than existing methods. This is accomplished by iteratively solving a lifting problem, which consists of a maximum weighted stable set problem on a smaller graph. Computational experience on DIMACS benchmark instances shows that the proposed approach may be a useful tool for generating cuts for the stable set polytope.