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<p><it>Abstract</it>—A self-routing multi-log<it>N</it> permutation network is presented and studied. This network has 3log<sub>2</sub><it>N</it>− 2 depth and <math><tmath>$N(\log_2^\gamma N)$</tmath></math>(3log<sub>2</sub>, <it>N</it>− 2)/2 nodes, where <it>N</it> is the number of network inputs and γ a constant very close to 1. A parallel routing algorithm runs in 3log<sub>2</sub><it>N</it>− 2 time on this network. The overall system (network and algorithm) can work in pipeline and it is asymptotically nonblocking in the sense that its blocking probability vanishes when <it>N</it> increases, hence the quasi-totality of the information synchronously arrives in 3log<sub>2</sub><it>N</it>− 2 steps at the network outputs. This network presents very good fault tolerance, a modular architecture, and it is suitable for information exchange in very large scale parallel processors and communication systems.</p>
Permutation networks, self-routing algorithm, blocking probability, stack of banyan networks.
C. Ferrone, G.a. De Biase, A. Massini, "An O(log2 N) Depth Asymptotically Nonblocking Self-Routing Permutation Network", IEEE Transactions on Computers, vol. 44, no. , pp. 1047-1051, August 1995, doi:10.1109/12.403721
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