Covering random points in a unit disk

被引：1

作者：

Hansen, Jennie C. ^{[1
,2
]}

Schmutz, Eric ^{[3
]}

Sheng, Li ^{[3
]}

机构：

[1] Heriot Watt Univ, Actuarial Math & Stat Dept, Edinburgh EH14 4AS, Midlothian, Scotland

[2] Heriot Watt Univ, Maxwell Inst Math Sci, Edinburgh EH14 4AS, Midlothian, Scotland

[3] Drexel Univ, Dept Math, Philadelphia, PA 19104 USA

来源：

ADVANCES IN APPLIED PROBABILITY | 2008年 / 40卷 / 01期

关键词：

dominating set; random geometric graph; unit ball graph;

D O I：

10.1239/aap/1208358884

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Let D be the punctured unit disk. It is easy to see that no pair x, y in D can cover D in the sense that D cannot be contained in the union of the unit disks centred at x and y. With this fact in mind, let V-n = {X-1, X-2, ..., X-n}, where X-1, X-2, ... are random points sampled independently from a uniform distribution on D. We prove that, with asymptotic probability 1, there exist two points in V-n, that cover all of V-n.

引用

页码：22 / 30

页数：9

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