Branched Polyhedral Systems

We introduce the framework of polyhedral branching 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 [10]). Using the framework, we construct extended formulations for full orbitopes (the convex hulls of all 0/1-matrices with lexicographically sorted columns), we show at the examples of two special matching problems, how polyhedral branching 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 polyhedral branching systems.

• Type: Conference
• Year: 2010
• Where: IPCO
• Authors: Volker Kaibel, Andreas Loos
• Keywords: Convex Hulls, Extended Formulations, IPCO 2010, Optimization, Polyhedral Branching Systems