Constructing the City Voronoi Diagram Faster
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International Journal of Computational Geometry and Applications 18 (4): 275--294 (2008)

Given a set $P$ of $n$ point sites in the plane, the city Voronoi diagram subdivides 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 trans- portation network that consists of $c$ non-intersecting axis-parallel line segments. We describe an algorithm that constructs the city Voronoi diagram (including quickest path information) using $O((c + n) polylog(c + n))$ time and storage by means of a wavefront expansion. For $c Ømega(n łog^3 n)$ our algorithm is faster than an algorithm by Aichholzer et al., which takes $O(n n + c^2 c)$ time.
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