A mathematical for periodic scheduling problems
SIAM Journal on Discrete Mathematics
Branch-And-Price: Column Generation for Solving Huge Integer Programs
Operations Research
Packing and partitioning orbitopes
Mathematical Programming: Series A and B
A Branch-and-Cut algorithm for graph coloring
Discrete Applied Mathematics - Special issue: IV ALIO/EURO workshop on applied combinatorial optimization
Automatic Generation of Symmetry-Breaking Constraints
COCOA 2008 Proceedings of the 2nd international conference on Combinatorial Optimization and Applications
The maximum k-colorable subgraph problem and orbitopes
Discrete Optimization
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We define a fundamental domain of a linear programming relaxation of a combinatorial integer program which is symmetric under a group action. We then provide a construction for the polytope of a fundamental domain defined by the maximization of a linear function. The computation of this fundamental domain is at worst polynomial in the size of the group. However, for the special case of the symmetric group, whose size is exponential in the size of the integer program, we show how to compute a separating hyperplane in polynomial time in the size of the integer program. Fundamental domains may provide a straightforward way to reduce the computation difficulties that often arise in integer programs with symmetries. Our construction is closely related to the constructions of orbitopes by Kaibel and Pfetch, but are simpler and more general, at a cost of creating new non-integral extreme points.