Faenza, Y.
Kaibel, V.
Extended Formulations for Packing and Partitioning Orbitopes
Mathematics of Operations Research
1526-5471
10.1287/moor.1090.0392
34
3
686-697
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 [Kaibel, V., M. E. Pfetsch. 2008. Packing and partitioning orbitopes. Math. Programming, Ser. A 114(1) 1–36]. These polytopes are the convex hulls of all 0/1-matrices with lexicographically sorted columns and at most, respectively, 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 established in the paper mentioned above, that basically shifted-column inequalities suffice to describe those orbitopes linearly.
polytope;
symmetry;
projection;
shifted-column inequalities;
extended formulation;
2009
http://infoscience.epfl.ch/record/181874/files/0806.0233v1.pdf;