On the behavior of the image-operator under blocker duality

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