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arXiv · 1302.2340

On the extension complexity of combinatorial polytopes

David Avis·Hans Raj Tiwary
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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.

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David Avis, Hans Raj Tiwary. 2013-02-10. On the extension complexity of combinatorial polytopes. https://arxiv.org/abs/1302.2340

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