### Abstract

We prove tight bounds on the complexity of bisectors and Voronoi diagrams on so-called realistic terrains, under the geodesic distance. In particular, if n denotes the number of triangles in the terrain, we show the following two results. (i) If the triangles of the terrain have bounded slope and the projection of the set of triangles onto the xy-plane has low density, then the worst-case complexity of a bisector is Θ(n). (ii) If, in addition, the triangles have similar sizes and the domain of the terrain is a rectangle of bounded aspect ratio, then the worst-case complexity of the Voronoi diagram of m point sites is Θ(n +m√n).

Original language | English (US) |
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Title of host publication | Algorithms - ESA 2008 - 16th Annual European Symposium, Proceedings |

Pages | 100-111 |

Number of pages | 12 |

DOIs | |

State | Published - 2008 |

Event | 16th Annual European Symposium on Algorithms, ESA 2008 - Karlsruhe, Germany Duration: Sep 15 2008 → Sep 17 2008 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 5193 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 16th Annual European Symposium on Algorithms, ESA 2008 |
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Country | Germany |

City | Karlsruhe |

Period | 9/15/08 → 9/17/08 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Algorithms - ESA 2008 - 16th Annual European Symposium, Proceedings*(pp. 100-111). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5193 LNCS). https://doi.org/10.1007/978-3-540-87744-8-9