Abstract
Derives a simple lower bound for performing a 2/sup b/ permutation on an N-PE SIMD hypercube, proving that log N-b routing steps are needed even if one allows an arbitrary mapping of elements to processors. An algorithm for performing a 2/sup b/ permutation using exactly log N-b full-duplex routing steps that is slightly more efficient than previously known O(log N-b) algorithms, which perform the permutation as an Omega or Omega /sup -1/ mapping, is presented. The author has also identified a general class of parallel computations called +or-2/sup b/ descend, which includes Batcher's odd-even merge and many other algorithms. An efficient algorithm for performing any computation in this class in O(log N) steps on an N-PE SIMD hypercube is given. A related class of parallel computations called +or-2/sup b/ ascend is also defined. This class appears to be more difficult than +or-2/sup b/ descend. A simple O(log/sup 2/ N/log log) N algorithm for this class on a SIMD hypercube, requiring Theta (log log N) space per processor is developed. >
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