### 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} = {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}. © Applied Probability Trust 2008.

Original language | English |
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Pages (from-to) | 22-30 |

Number of pages | 9 |

Journal | Advances in Applied Probability |

Volume | 40 |

Issue number | 1 |

DOIs | |

Publication status | Published - Mar 2008 |

### Keywords

- Dominating set
- Random geometric graphy
- Unit ball graph

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## Cite this

Hansen, J. C., Schmutz, E., & Sheng, L. (2008). Covering random points in a unit disk.

*Advances in Applied Probability*,*40*(1), 22-30. https://doi.org/10.1239/aap/1208358884