Finite state model and compatibility theory: New analysis tools for permutation networks
In this paper, the authors 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=log/sub 2/N and N is the number of inputs and outputs interconnected by the network. They 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. Benes network is the most well-known network that can realize all permutations. To show the flexibility of the approach, the authors describe a general class of FPM, stack permutation machine (SPM), which can realize all permutations, and show that FPM corresponding to Benes network belongs to SPM. They also show that FPM corresponding to the network with 2 cascaded reverse-exchange networks can realize all permutations. To show the simplicity of the approach, they also present a very simple mechanism to verify several equivalence relationships of various permutation networks.
- Research Organization:
- System Design and Analysis Group, Dept. of Computer Science, Univ. of Maryland, College Park, MD 20742
- OSTI ID:
- 5404781
- Journal Information:
- IEEE Trans. Comput.; (United States), Vol. C-35:7
- Country of Publication:
- United States
- Language:
- English
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