## Abstract

Let P be a simple polygon, and let Q be a set of points in P. We present an almostlinear time algorithm for computing a minimum cover of Q by disks that are contained in P. We then generalize the algorithm so that it can compute a minimum cover of Q by homothets of any fixed compact convex set O of constant description complexity that are contained in P. This improves previous results of Katz and Morgenstern [Lecture Notes in Comput. Sci. 5664, 2009, pp. 447-458]. We also consider the minimum disk-cover problem when Q is contained in a (sufficiently narrow) annulus and present a nearly linear algorithm for this case, too.

Original language | English |
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Pages (from-to) | 1647-1661 |

Number of pages | 15 |

Journal | SIAM Journal on Computing |

Volume | 40 |

Issue number | 6 |

DOIs | |

State | Published - 1 Dec 2011 |

## Keywords

- Chordal graphs
- Geometric covering
- Minimum disk cover

## ASJC Scopus subject areas

- General Computer Science
- General Mathematics