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Random half-integral polytopes

Gábor Braun (braung***at***renyi.hu)
Sebastian Pokutta (pokutta***at***mit.edu)

Abstract: We show that half-integral polytopes obtained as the convex hull of a random set of half-integral points of the 0/1 cube have rank as high as Ω(logn/loglogn) with positive probability — even if the size of the set relative to the total number of half-integral points of the cube tends to 0. The high rank is due to certain obstructions. We determine the exact threshold number, when these obstructions cease to exist.

Keywords: combinatorial optimization, admissible cutting-plane procedures, random polytopes, integer programming

Category 1: Integer Programming (Cutting Plane Approaches )

Category 2: Integer Programming (0-1 Programming )

Category 3: Combinatorial Optimization (Polyhedra )

Citation:

Download: [PDF]

Entry Submitted: 11/13/2010
Entry Accepted: 11/14/2010
Entry Last Modified: 03/06/2011

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