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Issue No. 07 - July (1986 vol. 35)
ISSN: 0018-9340
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.
tightly coupled multiprocessors, Finite permutation machine, interconnection network, permutation network, shuffle, SIMD, stack permutation machine

S. Tripathi and n. Shing-Tsaan Huang, "Finite State Model and Compatibility Theory: New Analysis Tools for Permutation Networks," in IEEE Transactions on Computers, vol. 35, no. , pp. 591-601, 1986.
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