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- W2001211700 abstract "Using a divide, prune, and conquer approach based on geometric partitioning, we obtain: (1) An output sensitive algorithm for computing a weighted Voronoi diagram inR4 (the projection of certain polyhedra inR5) that runs in time O((n+ f) log3 f) where n is the number of sites and f is the number of output cells; and (2) a deterministic parallel algorithm in the EREW PRAM model for computing an algebraic planar Voronoi diagram (in which bisectors between sites are simple curves consisting of a constant number of algebraic pieces of constant degree) that runs in time O(log2 n) using optimal O(n logn) work. The first result implies an algorithm for the problems of computing the convex hull of a point set and the intersection of a set of halfspaces inR5, and computing the Euclidean Voronoi diagram in R4. The second result implies both sequential and parallel work-optimal deterministic algorithms for a number of Voronoi diagram problems (including line segments in the plane), and other non-Voronoi diagram problems that can fit in the framework (including the intersection of equal radius balls in R3 and some lower envelope problems inR3)." @default.
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- W2001211700 date "1996-01-01" @default.
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- W2001211700 title "On computing Voronoi diagrams by divide-prune-and-conquer" @default.
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