The Minor inequalities in the description of the Set Covering Polyhedron of Circulant Matrices

In this work we give a complete description of the set covering polyhedron of circulant matrices $C^k_{sk}$ with $s = 2,3$ and $k\geq 3$ by linear inequalities. In particular, we prove that every non boolean facet defining inequality is associated with a circulant minor of the matrix. We also give a polynomial time separation algorithm for inequalities involved in the description.Comment: 17 pages, 5 figure

Some advances on the set covering polyhedron of circulant matrices

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.Comment: 20 pages, 2 figure