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

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