Semigroup computation and its applications on mesh-connected computers with hyperbus broadcasting

Let /spl oplus/ be an associative operation on a domain D. The semigroup problem is to compute a/sub 0//spl oplus/a/sub 1//spl oplus/...a/sub N-1/, where a/sub i/ /spl isin/D, for 0/spl les/i<N. The algorithm described here runs on SIMD mesh-connected computers with hyperbus broadcasting using p processors in time O(N/p+logp), where p/spl les/N. It as shown optimal when p=N and optimal speedup when p log p=N. Based on the proposed semigroup algorithm, other applications such as matrix multiplication, all-pair shortest path, shortest path spanning tree, topological sorting and connected component problems can be also solved in the order of logarithmic time using N/sup 3/ processors.

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