Schreier-Sims Cuts meet Stable Set: Preserving Problem Structure when Handling Symmetries

TL;DR

This paper investigates the use of Schreier-Sims cuts (SST cuts), a type of symmetry handling inequality, in integer programming, especially for the stable set problem, demonstrating their computational benefits and structural preservation.

Contribution

It introduces new presolving techniques and strengthened SST cuts for the stable set problem, showing they do not increase complexity and can improve problem solving efficiency.

Findings

SST cuts do not increase computational complexity.

Presolving techniques based on SST cuts are effective.

Strengthened SST cuts can maintain integrality in certain cases.

Abstract

Symmetry handling inequalities (SHIs) are a popular tool to handle symmetries in integer programming. Despite their successful application in practice, only little is known about the interaction of SHIs with optimization problems. In this article, we focus on SST cuts, an attractive class of SHIs, and investigate their computational and polyhedral consequences for optimization problems. After showing that they do not increase the computational complexity of solving optimization problems, we focus on the stable set problem for which we derive presolving techniques based on SST cuts. Moreover, we derive strengthened versions of SST cuts and identify cases in which adding these inequalities to the stable set polytope maintains integrality. Preliminary computational experiments show that our techniques have a high potential to reduce both the size of stable set problems and the time to solve them.