Abstract Voronoi Diagrams from Closed Bisecting Curves

We present the first algorithm for constructing abstract Voronoi diagrams from bisectors that are unbounded or closed Jordan curves. It runs in expected O(s2nlog(max{s,n}) ∑i=2nm i/i) many steps and O(∑i=3nm i) space, where n is the number of sites, mi denotes the average number of faces (connected components) per Voronoi region in any diagram of a subset of i sites, and s is the maximum number of intersection points between any two related bisectors.

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