On the extension complexity of combinatorial polytopes

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.

15 pages, 3 figures, 2 tables

References in corpus (1)

• Some 0/1 polytopes need exponential size extended formulations

Cited by in corpus (7)

• The matching polytope has exponential extension complexity
• A special role of Boolean quadratic polytopes among other combinatorial polytopes
• Extension Complexity, MSO Logic, and Treewidth
• Generalised probabilistic theories and conic extensions of polytopes
• Lower Bounds on the Sizes of Integer Programs Without Additional Variables
• A generalization of extension complexity that captures $P$
• On the H-Free Extension Complexity of the TSP