Random half-integral polytopes

被引：1

作者：

Braun, Gabor ^{[2
]}

Pokutta, Sebastian ^{[1
]}

机构：

[1] Univ Erlangen Nurnberg, Dept Math, D-91058 Erlangen, Germany

[2] Alfred Renyi Inst Math, H-1053 Budapest, Hungary

来源：

OPERATIONS RESEARCH LETTERS | 2011年 / 39卷 / 03期

关键词：

Random half-integral polytopes; Cutting-plane procedures; Rank lower bounds; RANK;

D O I：

10.1016/j.orl.2011.03.003

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

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 Omega(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 those cease to exist. (C) 2011 Elsevier B.V. All rights reserved.

引用

页码：204 / 207

页数：4

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