Polyhedral characterization of discrete dynamic programming
Operations Research
Packing and partitioning orbitopes
Mathematical Programming: Series A and B
Network Formulations of Mixed-Integer Programs
Mathematics of Operations Research
Extended Formulations for Packing and Partitioning Orbitopes
Mathematics of Operations Research
Symmetry matters for the sizes of extended formulations
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Constructing extended formulations from reflection relations
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
Separating stable sets in claw-free graphs via Padberg-Rao and compact linear programs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Symmetry matters for the sizes of extended formulations
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
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We introduce the framework of branched polyhedral systems that can be used in order to construct extended formulations for polyhedra by combining extended formulations for other polyhedra. The framework, for instance, simultaneously generalizes extended formulations like the well-known ones (see Balas [1]) for the convex hulls of unions of polyhedra (disjunctive programming) and like those obtained from dynamic programming algorithms for combinatorial optimization problems (due to Martin, Rardin, and Campbell [11]). Using the framework, we construct extended formulations for full orbitopes (the convex hulls of all 0/1-matrices with lexicographically sorted columns), we show for two special matching problems, how branched polyhedral systems can be exploited in order to construct formulations for certain nested combinatorial problems, and we indicate how one can build extended formulations for stable set polytopes using the framework of branched polyhedral systems.