On the extension complexity of combinatorial polytopes

Authors:
David Avis;Hans Raj Tiwary
Affiliations:
GERAD and School of Computer Science, McGill University, Montreal, Quebec, Canada,Graduate School of Informatics, Kyoto University, Kyoto, Japan;Department of Mathematics, Université Libre de Bruxelles, Brussels, Belgium
Venue:
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Year:
2013

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Abstract

In this paper we extend recent results of Fiorini et al. on the extension complexity of the cut polytope and related polyhedra. We first describe a lifting argument to show exponential extension complexity for a number of NP-complete problems including subset-sum and three dimensional matching. We then obtain a relationship between the extension complexity of the cut polytope of a graph and that of its graph minors. Using this we are able to show exponential extension complexity for the cut polytope of a large number of graphs, including those used in quantum information and suspensions of cubic planar graphs.