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Finite State Model and Compatibility Theory: New Analysis Tools for Permutation Networks
July 1986 (vol. 35 no. 7)
pp. 591-601
null Shing-Tsaan Huang, System Design and Analysis Group, Department of Computer Science, University of Maryland
In this paper, we present a new model, finite permutation machine (FPM), to describe the permutation networks. A set of theorems are developed to capture the theory of operations for the permutation networks. Using this new framework, an interesting problem is attacked: are 2n - 1 passes of shuffle exchange necessary and sufficient to realize all permutations? where n = log2 N and N is the number of inputs and outputs interconnected by the network. We prove that to realize all permutations, 2n - 1 passes of shuffle exchange are necessary and that 3n - 3 passes are sufficient. This reduces the sufficient number of passes by 2 from the best-known result.
Index Terms:
tightly coupled multiprocessors, Finite permutation machine, interconnection network, permutation network, shuffle, SIMD, stack permutation machine
Citation:
null Shing-Tsaan Huang, S.K. Tripathi, "Finite State Model and Compatibility Theory: New Analysis Tools for Permutation Networks," IEEE Transactions on Computers, vol. 35, no. 7, pp. 591-601, July 1986, doi:10.1109/TC.1986.1676800
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