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A Theoretical Study of Parallel Voronoi Diagram

In this paper, we concentrate on the problem of computing a Voronoi diagram using Hypercube model of computation. The main contribution of this work is the O(log n) parallel algorithm for computing Voronoi diagram on the Euclidean plane. Our technique parallelizes the wellknown seemingly inherent sequential technique of Shamos and Hoey, and makes use of a number of special properties of the dividing polygonal chain and the Batchers bitonic sort.