arXiv subjects

Paola B. Tolomei

Publications and source records attributed to Paola B. Tolomei.

4 recordsLinked to original sources

arXiv2018

Addendum to Vertex adjacencies in the set covering polyhedron

We study the relationship between the vertices of an up-monotone polyhedron $R$ and those of the polytope $P$ obtained by truncating $R$ with the unit hypercube. When $R$ has binary vertices, we characterize the vertices of $P$ in terms of the vertices of $R$, show their integrality, and prove that the 1-skeleton of $R$ is an induced subgraph of the 1-skeleton of $P$. We conclude by applying our findings to settle a claim in the original paper.

math.CO↗

arXiv2017

Vertex adjacencies in the set covering polyhedron

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.

math.CO↗

arXiv2014

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

We study the set covering polyhedron related to circulant matrices. In particular, our goal is to characterize the first Chvátal 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.

math.CO↗

arXiv2012

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.

math.CO↗