KISSING POLYTOPES

被引：0

作者：

Deza, Antoine ^{[1
]}

Onn, Shmuel ^{[2
]}

Pokutta, Sebastian ^{[3
]}

Pournin, Lionel ^{[4
]}

机构：

[1] McMaster Univ, Hamilton, ON L8S 4L8, Canada

[2] Technion Israel Inst Technol, IL-32000 Haifa, Israel

[3] Zuse Inst Berlin, Berlin, Germany

[4] Univ Paris 13, Villetaneuse, France

来源：

SIAM JOURNAL ON DISCRETE MATHEMATICS | 2024年 / 38卷 / 04期

基金：

美国国家科学基金会; 以色列科学基金会; 加拿大自然科学与工程研究理事会;

关键词：

facial distance; vertex-facet distance; pyramidal width; alternating projections; distances in geometric lattices; lattice polytopes;

D O I：

10.1137/24M1640859

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate the following question: How close can two disjoint lattice polytopes contained in a fixed hypercube be? This question stems from various contexts where the minimal distance between such polytopes appears in complexity bounds of optimization algorithms. We provide nearly matching bounds on this distance and discuss its exact computation. We also give similar bounds for disjoint rational polytopes whose binary encoding length is prescribed.

引用

页码：2643 / 2664

页数：22

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