2014
DOI: 10.1007/s00454-014-9655-9
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A Short Proof that the Extension Complexity of the Correlation Polytope Grows Exponentially

Abstract: We establish that the extension complexity of the n × n correlation polytope is at least 1.5n 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 uniquedisjointness predicate is at … Show more

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Cited by 48 publications
(34 citation statements)
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“…In particular, Theorem 1.2 immediately follows from the following result. We remark that this is a generalization of a result in [16], where the case t = 1 was established.…”
Section: Our Resultssupporting
confidence: 69%
“…In particular, Theorem 1.2 immediately follows from the following result. We remark that this is a generalization of a result in [16], where the case t = 1 was established.…”
Section: Our Resultssupporting
confidence: 69%
“…The factor log(3/2) ≈ 0.585 in the exponent is the current best one due to [16]; for various approximate case versions see [3,5,7]. The first exponential lower bound was established in [12,13] by combining the seminal work of [20] together with an observation in [24].…”
Section: Unique Disjointnessmentioning
confidence: 98%
“…Finally, since K h is a minor of K h,h , we have xc(COR(K h )) xc(COR(K h,h )). In [12], it is shown that xc(COR(K h )) (1.5) h . (A weaker exponential bound was given earlier in [9].)…”
Section: Proof It Is Easy To See That Hmentioning
confidence: 99%