Faenza, Y.
Kaibel, V.
Extended Formulations for Packing and Partitioning Orbitopes
Mathematics of Operations Research
Mathematics of Operations Research
Mathematics of Operations Research
Mathematics of Operations Research
34
3
polytope
symmetry
projection
shifted-column inequalities
extended formulation
2009
2009
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.
1526-5471
Mathematics of Operations Research
Journal Articles
10.1287/moor.1090.0392