A randomized algorithm for Voronoi diagram of line segments on coarse grained multiprocessors

We present a randomized parallel algorithm for the Voronoi diagram of line segments on coarse grained parallel machines, which, for any input of n line segments on P processors (n=Ω(P^3+ε), for any ε>0) requires (with high probability) O([n log n/P]) local operations, O(n/P) global-operations (or messages) per processor, O(1) levels of global data dependency (or O(1) communication phases). This generic parallel algorithm can be transformed to the CRCW PRAM model in O(log n) time with O(n) processors and thus provides a different solution from, and conceptually much simpler than, that of (Rajasekaran, 1994)