Constructing the city Voronoi diagram faster

R. Görke, A. Wolff

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    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 languageEnglish
    Title of host publicationProceedings 2nd International Symposium on Voronoi Diagrams in Science and Engineering (VD'05, Seoul, Korea, October 10-13, 2005)
    Publication statusPublished - 2005


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