Computational geometry: an introduction
Computational geometry: an introduction
Parallel algorithms for geometric problems
Parallel algorithms for geometric problems
SFCS '75 Proceedings of the 16th Annual Symposium on Foundations of Computer Science
Parallel computational geometry
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
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While constructing a Voronoi diagram V"P for a set P of n points on a mesh-connected computer (MCC), it is necessary to find a set B of edges which are intersected by the dividing chain C during the merge process of two Voronoi diagrams V"L and V"R, where L and R contain the leftmost [n/2] points and the rightmost [n/2] points of P respectively. The computation of B requires two operations: First decide for each edge e in V"L and V"R whether its end vertices are closer to L or R, and then from that information, determine whether e is intersected by C. However, in the previous parallel algorithm each of the former and latter operations requires planar point location which takes O(@/n) time on a @/n x @/n MCC, and in addition the former operation needs to compute convex hulls of L and R. In this paper, we shall show that the latter operation can be done in O(1) time without executing planar point location and the former operation can be executed without the computation of convex hulls. Therefore, the computation of B is reduced to only one planar point location.