Covering random points in a unit disk

Jennie C. Hansen, Eric Schmutz, Li Sheng

Research output: Contribution to journalArticle

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 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. © Applied Probability Trust 2008.

Original languageEnglish
Pages (from-to)22-30
Number of pages9
JournalAdvances in Applied Probability
Volume40
Issue number1
DOIs
Publication statusPublished - Mar 2008

Keywords

  • Dominating set
  • Random geometric graphy
  • Unit ball graph

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