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A parallel algorithm to determine the switch settings for a Benes permutation network is developed. This algorithm can determine the switch settings for an N input/output Benes network in 0(log2N) time when a fully interconnected parallel computer with N processing elements is used. The algorithm runs in 0(N½) time on an N½× N½mesh-connected computer and 0(log4N) time on both a cube connected and a perfect shuffle computer with N processing elements. It runs in 0(k log3N) time on cube connected and perfect shuffle computers with N1+1/kprocessing elements.