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<p>Derives a simple lower bound for performing a 2/sup b/ permutation on an N-PE SIMDhypercube, proving that log N-b routing steps are needed even if one allows an arbitrarymapping of elements to processors. An algorithm for performing a 2/sup b/ permutationusing exactly log N-b full-duplex routing steps that is slightly more efficient thanpreviously known O(log N-b) algorithms, which perform the permutation as an Omega orOmega /sup -1/ mapping, is presented. The author has also identified a general class ofparallel computations called +or-2/sup b/ descend, which includes Batcher's odd-evenmerge 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.</p>
Index Terms2/sup b/ permutation; SIMD hypercube; routing steps; full-duplex routing; parallelcomputations; efficient algorithm; +or-2/sup b/ ascend; +or-2/sup b/ descend; cyclicshift; odd-even merge; parallel prefix; PM2I interconnection; computational complexity;hypercube networks; parallel algorithms

D. Nassimi, "Parallel Algorithms for the Classes of +or-2^b DESCEND and ASCEND Computations on a SIMD Hypercube," in IEEE Transactions on Parallel & Distributed Systems, vol. 4, no. , pp. 1372-1381, 1993.
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