Covering random points in a unit disk

Jennie C. Hansen; Eric Schmutz; Li Sheng

doi:10.1239/aap/1208358884

Covering random points in a unit disk

Jennie C. Hansen, Eric Schmutz, Li Sheng

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

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 = {X₁, X₂,..., X_n}, where X₁, X₂,.... 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. © Applied Probability Trust 2008.

Original language	English
Pages (from-to)	22-30
Number of pages	9
Journal	Advances in Applied Probability
Volume	40
Issue number	1
DOIs	https://doi.org/10.1239/aap/1208358884
Publication status	Published - Mar 2008

Keywords

Dominating set
Random geometric graphy
Unit ball graph

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title = "Covering random points in a unit disk",

abstract = "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 Vn = \{X1, X2,..., Xn\}, where X1, X2,.... are random points sampled independently from a uniform distribution on D. We prove that, with asymptotic probability 1, there exist two points in Vn that cover all of Vn. {\textcopyright} Applied Probability Trust 2008.",

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KW - Dominating set

KW - Random geometric graphy

KW - Unit ball graph

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JO - Advances in Applied Probability

JF - Advances in Applied Probability

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ER -

Covering random points in a unit disk

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Keywords

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