Note: On the behavior of the N+-operator under blocker duality

Authors:
Silvia M. Bianchi;Mariana S. Escalante;Graciela L. Nasini
Affiliations:
Universidad Nacional de Rosario, Argentina;Consejo Nacional de Investigaciones Científicas y Técnicas, Argentina and Universidad Nacional de Rosario, Argentina;Consejo Nacional de Investigaciones Científicas y Técnicas, Argentina and Universidad Nacional de Rosario, Argentina
Venue:
Discrete Applied Mathematics
Year:
2011

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Abstract

In this work we consider the Lovasz and Schrijver N"+-rank (Lovasz and Schrijver, 1991) [12] of set covering polytopes. In particular, we prove that given any positive integer number k there is a 0, 1 matrix for which the N"+-rank of its set covering polyhedron and the N"+-rank of the set covering polyhedron of its blocker differ by at least k. This shows the contrast between the behavior of the N"+ procedure and the disjunctive procedure observed in Aguilera et al. (2002) [2].