A fast parallel algorithm for routing in permutation networks

An algorithm is given for routing in permutation networks-that is, for computing the switch settings that implement a given permutation. The algorithm takes serial time <i>O</i>(<i>n</i>(log <i>N</i>)<sup>2</sup>) (for one processor with random access to a memory of <i>O</i>(<i>n</i>) words) or parallel time <i>O</i>((log <i>n</i>)<sup>3</sup>) (for <i>n</i> synchronous processors with conflict-free random access to a common memory of <i>O</i>(<i>n</i>) words). These time bounds may be reduced by a further logarithmic factor when all of the switch sizes are integral powers of two.

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