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. , which takes O(n log n+c2 log c) time.
|Journal||International Journal of Computational Geometry and Applications|
|Publication status||Published - 2008|