IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
Automatic Generation of Symmetry-Breaking Constraints
COCOA 2008 Proceedings of the 2nd international conference on Combinatorial Optimization and Applications
Solving Lot-Sizing Problems on Parallel Identical Machines Using Symmetry-Breaking Constraints
INFORMS Journal on Computing
Improving Bounds on the Football Pool Problem by Integer Programming and High-Throughput Computing
INFORMS Journal on Computing
Hard multidimensional multiple choice knapsack problems, an empirical study
Computers and Operations Research
Extended Formulations for Packing and Partitioning Orbitopes
Mathematics of Operations Research
Fundamental domains for integer programs with symmetries
COCOA'07 Proceedings of the 1st international conference on Combinatorial optimization and applications
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
Branch-cut-and-propagate for the maximum k-colorable subgraph problem with symmetry
CPAIOR'11 Proceedings of the 8th international conference on Integration of AI and OR techniques in constraint programming for combinatorial optimization problems
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
The maximum k-colorable subgraph problem and orbitopes
Discrete Optimization
A polyhedral approach for the equitable coloring problem
Discrete Applied Mathematics
Employee workload balancing by graph partitioning
Discrete Applied Mathematics
| Hi-index | 0.00 |
We introduce orbitopes as the convex hulls of 0/1-matrices that are lexicographically maximal subject 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 1-entry 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 well-known 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 facet-defining 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. The associated separation problems can be solved in linear time.