New parallel algorithms for convex hull and triangulation in 3-dimensional space
Let S be a set of n given points in 3-dimensional space. We present parallel algorithms for the construction of the convex hull and for triangulation of S on a CREW-PRAM. For 3-dim. convex hull our algorithm is time-optimal and uses time O(1/ε· log(n)) with O(n 1+e) processors. By duality parallel convex hull algorithms induce new ones for Voronoidiagrams in the plane, using the same time and processor bounds. A second parallel algorithm for Voronoi-diagrams presented here uses time O(log(n) 2) with O(n) processors.
For 3-dim. triangulation of S we give the first parallel algorithm for the generalized problem, using time O(log(n) 2) with O(n 1+e) processors. For the tangential-plane problem we give a parallel algorithm, needing time O(log(n)) with O(n) processors.
KeywordsConvex Hull Parallel Algorithm Vertex Versus Internal Edge Convex Hull Algorithm
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