An efficient parallel algorithm for the assignment problem on the plane

The authors consider a parallel algorithm for minimum weight perfect matching on complete bipartite graphs induced by two disjoint sets of points on the plane. The algorithm is designed for the EREW PRAM or EREW RPRAM model of parallel computation with p (a function of n) processors. For points on the Euclidean plane, the algorithm executes in O(n/sup 3//p/sup 2/+n/sup 2/ log n+n/sup 2.5/ log n/p) time for p< square root n. They achieve a perfect speedup algorithm when p>or= square root n/log n and square root n/p is not a constant.<
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