Random half-integral polytopes

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(log n/ log log n) 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.

• Type: Journal
• Year: 2011
• Where: ORL
• Authors: Gábor Braun, Sebastian Pokutta
• Keywords: Convex Hull, Integral Points, Operations Research, ORL 2011, Threshold Number