Some advances on the set covering polyhedron of circulant matrices

TL;DR

This paper extends the understanding of the set covering polyhedron for circulant matrices by generalizing facet-defining inequalities and providing polynomial algorithms for their separation.

Contribution

It broadens previous results to include all circulant minors and develops efficient algorithms for identifying these inequalities.

Findings

Extended facet-defining inequalities to all circulant minors.

Developed polynomial-time separation algorithms for specific inequality classes.

Enhanced the theoretical framework for the set covering polyhedron of circulant matrices.

Abstract

Working on the set covering polyhedron of consecutive ones circulant matrices, Argiroffo and Bianchi found a class of facet defining inequalities, induced by a particular family of circulant minors. In this work we extend these results to inequalities associated with every circulant minor. We also obtain polynomial separation algorithms for particular classes of such inequalities.