Vertex adjacencies in the set covering polyhedron

TL;DR

This paper characterizes vertex adjacencies in the set covering polyhedron, providing conditions for adjacency and applying these to identify a new family of minimally nonideal matrices.

Contribution

It introduces a new characterization of vertex adjacency in the set covering polyhedron and extends the understanding to row circular matrices.

Findings

Sufficient conditions for vertex adjacency in the set covering polyhedron.

Characterization of adjacency conditions for row circular matrices.

Identification of a new infinite family of minimally nonideal matrices.

Abstract

We describe the adjacency of vertices of the (unbounded version of the) set covering polyhedron, in a similar way to the description given by Chvatal for the stable set polytope. We find a sufficient condition for adjacency, and characterize it with similar conditions in the case where the underlying matrix is row circular. We apply our findings to show a new infinite family of minimally nonideal matrices.