Efficient Schemes for Parallel Communication

A family of balanced communication schemes for connecting N processors with only a constant number of lines entering or leaving each processor is defined. It is proved that this network topology enables a fully distributed probabilistic algorithm to execute a variety of communication requests efficiently. In particular it enables implementation of an arbitrary permutation, that is, a set of N packets initially located in distinct processors and destined for distinct destinations in O(log/sub 2/N) steps. Similar results are proved for randomly generated communication requests. These results suggest an efficient solution to a fundamental problem in the design of parallel computers.

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