A hierarchy of relaxation between the continuous and convex hull representations
SIAM Journal on Discrete Mathematics
Pruning by Isomorphism in Branch-and-Cut
Proceedings of the 8th International IPCO Conference on Integer Programming and Combinatorial Optimization
Improving Discrete Model Representations via Symmetry Considerations
Management Science
Exploiting structure in symmetry detection for CNF
Proceedings of the 41st annual Design Automation Conference
Improved Bounds for the Crossing Numbers of Km,n and Kn
SIAM Journal on Discrete Mathematics
Reduction of symmetric semidefinite programs using the regular $$\ast$$-representation
Mathematical Programming: Series A and B
Optimizing over the first Chvátal closure
Mathematical Programming: Series A and B
Optimizing over the split closure
Mathematical Programming: Series A and B
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
Improving Bounds on the Football Pool Problem by Integer Programming and High-Throughput Computing
INFORMS Journal on Computing
Mathematical Programming: Series A and B
Mathematical Programming: Series A and B
On the separation of disjunctive cuts
Mathematical Programming: Series A and B
Lexicography and degeneracy: can a pure cutting plane algorithm work?
Mathematical Programming: Series A and B
Reformulations in mathematical programming: automatic symmetry detection and exploitation
Mathematical Programming: Series A and B
New code upper bounds from the Terwilliger algebra and semidefinite programming
IEEE Transactions on Information Theory
Solving large Steiner Triple Covering Problems
Operations Research Letters
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In this paper we examine the impact of using the Sherali-Adams procedure on highly symmetric integer programming problems. Linear relaxations of the extended formulations generated by Sherali-Adams can be very large, containing $O(\binom{n}{d})$ many variables for the level-d closure. When large amounts of symmetry are present in the problem instance however, the symmetry can be used to generate a much smaller linear program that has an identical objective value. We demonstrate this by computing the bound associated with the level 1, 2, and 3 relaxations of several highly symmetric binary integer programming problems. We also present a class of constraints, called counting constraints, that further improves the bound, and in some cases provides a tight formulation.