Random half-integral polytopes

Authors:
GáBor Braun;Sebastian Pokutta
Affiliations:
Alfréd Rényi Institute of Mathematics, Budapest, Reáltanoda u. 13-15, 1053, Hungary;Friedrich-Alexander-University of Erlangen-Nürnberg, Department of Mathematics, Am Weichselgarten 9, 91058 Erlangen, Germany
Venue:
Operations Research Letters
Year:
2011

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Abstract

We show that polytopes obtained as the convex hull of a random set of half-integral points of the 0/1 cube have rank as high as @W(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 those cease to exist.