A fast selection algorithm for meshes with multiple broadcasting

One of the fundamental algorithmic problems in computer science involves selecting the kth smallest element in a collection A of n elements. We propose an algorithm design methodology to solve the selection problem on meshes with multiple broadcasting. Our methodology leads to a selection algorithm that runs in O(n/sup 1/8/(log n)/sup 3/4/)) time on a mesh with multiple broadcasting of size n/sup 3/8/(log n)/sup 1/4//spl times/n/sup 5/8//(log n)/sup 1/4/. This result is optimal over a large class of selection algorithms. Our result shows that just as for semigroup computations, selection can be done faster on suitably chosen rectangular meshes than on square meshes.<
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