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Abstract Voronoi diagrams were introduced by R . Klein [Kle89b, Kle88a, Kle88b] as an axiomatic basis ofVoronoi diagrams. We show how to construct abstract Voronoi diagrams in time O(nlogn) by a randomized algorithm, which is based on Clarkson and Shor's randomized incremental construction technique [CS89]. The new algorithm has the following advantages(More)
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)
3 Triangulation de Delaunay pleinement dynamique en temps moyen logarithmique par op eration Once upon a time was a Delaunay tree that wanted to get rid of some site p or murders in the Delaunay tree. a WADS Ao^ ut 91 a Ottawa (LNCS 519), a para ^ itre dans Computational Geometry Theory and Applications. Abstract The Delaunay Tree is a hierarchical data(More)