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Volker Kaibel (kaibelzib.de) Abstract: We introduce orbitopes as the convex hulls of 0/1matrices that are lexicographically maximal sub ject to a group acting on the columns. Special cases are packing and partitioning orbitopes, which arise from restrictions to matrices with at most or exactly one 1entry in each row, respectively. The goal of investigating these polytopes is to gain insight into ways of breaking certain symmetries in integer programs by adding constraints, e.g., for a wellknown formulation of the graph coloring problem. We provide a thorough polyhedral investigation of packing and partitioning orbitopes for the cases in which the group acting on the columns is the cyclic group or the symmetric group. Our main results are complete linear inequality descriptions of these polytopes by facetdefining inequalities. For the cyclic group case, the descriptions turn out to be totally unimodular, while for the symmetric group case both the description and the proof are more involved. Nevertheless, the associated separation problem can be solved in linear time also in this case. Keywords: integer programming, symmetry breaking, lexicographic representatives Category 1: Integer Programming (01 Programming ) Category 2: Combinatorial Optimization (Polyhedra ) Category 3: Integer Programming (Cutting Plane Approaches ) Citation: Report 0617, Zuse Institute Berlin, March 2006, 32 pages Download: [Compressed Postscript][PDF] Entry Submitted: 03/29/2006 Modify/Update this entry  
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