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Parallel algorithms for the classes of ±2b DESCEND and ASCEND computations on a SIMD hypercube

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1 Author(s)
Nassimi, D. ; Dept. of Comput. & Inf. Sci., New Jersey Inst. of Technol., Newark, NJ, USA

Derives a simple lower bound for performing a 2b 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 2b 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 Ω or Ω-1 mapping, is presented. The author has also identified a general class of parallel computations called ±2b 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 ±2b ascend is also defined. This class appears to be more difficult than ±2b descend. A simple O(log2 N/log log) N algorithm for this class on a SIMD hypercube, requiring Θ(log log N) space per processor is developed

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Parallel and Distributed Systems, IEEE Transactions on  (Volume:4 ,  Issue: 12 )