Zurück zu den Preprints des Jahres 2008


2008-10

Extended Formulations for Packing and Partitioning Orbitopes

by Faenza, Y., Kaibel, V..


Series: 2008-10, Preprints

MSC:
90C10 Integer programming

Abstract:
We give compact extended formulations for the packing and partitioning orbitopes (with respect to the full symmetric group) described and analyzed in (Kaibel and Pfetsch, 2008). These polytopes are the convex hulls of all 0/1-matrices with lexicographically sorted columns and at most, resp. exactly, one 1-entry per row. They are important objects for symmetry reduction in certain integer programs.
Using the extended formulations, we also derive a rather simple proof of the fact that basically shifted-column inequalities suffice in order to describe those orbitopes linearly.

Keywords:
symmetry, integer programming, polytop, lexicographical, orbitope, extended formulation