On the size of the largest empty box amidst a point set

被引：23
|
作者：
Aistleitner, Christoph [1 ]
Hinrichs, Aicke [2 ]
Rudolf, Daniel [3 ]
机构：
[1] Univ Linz, Inst Financial Math & Appl Number Theory, Linz, Austria
[2] Univ Linz, Inst Anal, Linz, Austria
[3] Univ Gottingen, Inst Math Stochast, Gottingen, Germany
来源：
DISCRETE APPLIED MATHEMATICS | 2017年 / 230卷
基金：
奥地利科学基金会;
关键词：
Dispersion; Largest empty box; Extremal discrepancy;
D O I：
10.1016/j.dam.2017.06.008
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The problem of finding the largest empty axis-parallel box amidst a point configuration is a classical problem in computational geometry. It is known that the volume of the largest empty box is of asymptotic order 1/n for n -> infinity and fixed dimension d. However, it is natural to assume that the volume of the largest empty box increases as d gets larger. In the present paper we prove that this actually is the case: for every set of n points in [0, l](d) there exists an empty box of volume at least c(d)n(-1), where cd -> infinity as d -> infinity. More precisely, cd is at least of order roughly log d. (C) 2017 Elsevier B.V. All rights reserved.
引用
收藏
页码：146 / 150
页数：5
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