Selection on rectangular meshes with multiple broadcasting

One of the fundamental algorithmic problems in computer science involves selecting thekth smallest element in a setS ofn elements. In this paper we present a fast selection algorithm which runs inO(n1/8 logn) time on a mesh with multiple broadcasting of sizen3/8 ×n5/8. Our result shows that, just like semigroup computations, selection can be done much faster on a suitably chosen rectangular mesh than on square meshes. We also show that if every processor can storen1/9 items, then our selection algorithm runs inO(n1/9 logn) time on a mesh with multiple broadcasting of sizen1/3 ×n5/9.

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