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A Short Proof that the Extension Complexity of the Correlation Polytope Grows Exponentially

Volker Kaibel(kaibel***at***ovgu.de)
Stefan Weltge(weltge***at***ovgu.de)

Abstract: We establish that the extension complexity of the nXn correlation polytope is at least 1.5^n by a short proof that is self-contained except for using the fact that every face of a polyhedron is the intersection of all facets it is contained in. The main innovative aspect of the proof is a simple combinatorial argument showing that the rectangle covering number of the unique-disjointness matrix is at least 1.5^n, and thus the nondeterministic communication complexity of the unique-disjointness predicate is at least .58n.

Keywords: lower bound, extension complexity, correlation polytope, unique disjointness, nondeterministic communication complexity

Category 1: Combinatorial Optimization (Polyhedra )

Category 2: Linear, Cone and Semidefinite Programming (Linear Programming )

Citation: August 2013

Download: [PDF]

Entry Submitted: 09/10/2013
Entry Accepted: 09/10/2013
Entry Last Modified: 09/10/2013

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