Silvia M. Bianchi

Lift and project relaxations for the matching and related polytopes

We compare lift and project methods given by Lovasz and Schrijver (the N+ and N procedures) and by Balas, Ceria and Cornuejols (the disjunctive procedure) when working on the matching, perfect matching and covering polytopes. When the underlying graph is the complete graph of n=2s + 1 nodes we obtain that the disjunctive index for all problems is s2, the N+-index for the matching and perfect matching problems is s (extending a result by Stephen and Tuncel), the N-index for the perfect matching problem is s, and the N+ and N indices for the covering problem and the N-index for the matching problem are strictly greater than s.

Some advances on the set covering polyhedron of circulant matrices

Studying 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.

Lovász-Schrijver SDP-operator and a superclass of near-perfect graphs

Abstract We study the Lovasz-Schrijver SDP-operator applied to the fractional stable set polytope of graphs. The problem of obtaining a combinatorial characterization of graphs for which the SDP-operator generates the stable set polytope in one step has been open since 1990. In an earlier publication, we named these graphs N + -perfect. In the current contribution, we propose a conjecture on combinatorial characterization of N + -perfect graphs and make progress towards such a full combinatorial characterization by establishing a new, close relationship among N + -perfect graphs, near-bipartite graphs and a newly introduced concept of full-support-perfect graphs.

Near-perfect graphs with polyhedral N+(G)

Abstract One of the beautiful results due to Grotschel, Lovasz and Schrijver is the fact that the theta body of a graph G is polyhedral if and only if G is perfect. Related to the theta body of G is a foundational construction of an operator on polytopes, called N + ( ⋅ ) , by Lovasz and Schrijver. Here, we initiate the pursuit of a characterization theorem analogous to the one above by Grotschel, Lovasz and Schrijver, replacing the theta body of G by N + ( G ) and searching for the combinatorial counterpart to replace the class of perfect graphs.

On a certain class of nonideal clutters

In this paper we define the class of near-ideal clutters following a similar concept due to Shepherd [Near perfect matrices, Math. Programming 64 (1994) 295-323] for near-perfect graphs. We prove that near-ideal clutters give a polyhedral characterization for minimally nonideal clutters as near-perfect graphs did for minimally imperfect graphs. We characterize near-ideal blockers of graphs as blockers of near-bipartite graphs. We find necessary conditions for a clutter to be near-ideal and sufficient conditions for the clutters satisfying that every minimal vertex cover is minimum.

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

The set covering problem on circulant matrices: polynomial instances and the relation with the dominating set problem on webs☆

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Clutter nonidealness

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