### Abstract

Given a set S of n point sites in the plane, the City Voronoi diagram partitions the plane into the Voronoi regions of the sites, with respect to the City metric. This metric is induced by quickest paths according to the Manhattan metric and an accelerating transportation network that consists of c non-intersecting axisparallel line segments. We describe an algorithm that constructs the City Voronoi diagram (including quickest path information) in O((c+n)polylog(c+n)) time using a wavefront expansion. For c ¿ O( vnlog3(n)) our algorithm is faster than an algorithm by Aichholzer et al. [2], which takes O(n log n+c2 log c) time.

Original language | English |
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Title of host publication | Abstracts 21th European Workshop on Computational Geometry (EWCG 2005, Eindhoven, The Netherlands, March 9-11, 2005) |

Editors | M.T. Berg, de |

Publisher | Technische Universiteit Eindhoven |

Pages | 155-158 |

Publication status | Published - 2005 |

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## Cite this

Görke, R., & Wolff, A. (2005). Constructing the city Voronoi diagram faster. In M. T. Berg, de (Ed.),

*Abstracts 21th European Workshop on Computational Geometry (EWCG 2005, Eindhoven, The Netherlands, March 9-11, 2005)*(pp. 155-158). Technische Universiteit Eindhoven.