Generalized minor inequalities for the set covering polyhedron related to circulant matrices

TL;DR

This paper characterizes the first Chvátal closure of the fractional relaxation of the set covering polyhedron associated with circulant matrices, introducing generalized minor inequalities and a polynomial-time separation algorithm.

Contribution

It introduces a family of generalized minor inequalities that extend previous results and provides a polynomial-time algorithm for separating a subfamily of these inequalities.

Findings

New facet-defining inequalities for the set covering polyhedron

A polynomial-time separation algorithm for a subfamily of inequalities

Enhanced understanding of the Chvátal closure in circulant matrix contexts

Abstract

We study the set covering polyhedron related to circulant matrices. In particular, our goal is to characterize the first Chv\'atal closure of the usual fractional relaxation. We present a family of valid inequalities that generalizes the family of minor inequalities previously reported in the literature and includes new facet-defining inequalities. Furthermore, we propose a polynomial time separation algorithm for a particular subfamily of these inequalities.