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Once upon a time was a Delaunay tree that wanted to get rid of some site p or murders in the Delaunay tree. Abstract The Delaunay Tree is a hierarchical data structure that has been introduced in 7] and analyzed in 6, 4]. For a given set of sites S in the plane and an order of insertion for these sites, the Delaunay Tree stores all the successive Delaunay(More)
Voronoi diagrams were introduced by R. Klein (1988) as an axiomatic basis of Voronoi diagrams. We show how to construct abstract Voronoi diagrams in time O(n log n) by a randomized algorithm, which is based on Clarkson and Shor's randomized incremental construction technique (1989). The new algorithm has the following advantages over previous algorithms: l(More)
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