Extended Formulations for Packing and Partitioning Orbitopes
Mathematics of Operations Research
Constructing extended formulations from reflection relations
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
Symmetry matters for the sizes of extended formulations
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Intermediate integer programming representations using value disjunctions
Discrete Optimization
| Hi-index | 0.00 |
Extended formulations are an important tool to obtain small (even compact) formulations of polytopes by representing them as projections of higher dimensional ones. It is an important question whether a polytope admits a small extended formulation, i.e., one involving only a polynomial number of inequalities in its dimension. For the case of symmetric extended formulations (i.e., preserving the symmetries of the polytope) Yannakakis established a powerful technique to derive lower bounds and rule out small formulations. We rephrase the technique of Yannakakis in a group-theoretic framework. This provides a different perspective on symmetric extensions and considerably simplifies several lower bound constructions.