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<p>The authors present an efficient routing algorithm for realizing any permutation in LIN (linear-permutation-class) on single-stage shuffle-exchange networks with k*k switching elements, where k=p is a prime number. For any positive integer number n there are N=k/sup n/ processors connected by the network. The proposed algorithm can realize LIN in 2n-1 passes; it can be implemented by using Nn processors in O(n) time. It can also be extended to the shuffle-exchange networks with (p/sup t/*p/sup t/) switching elements, where t is a positive integer number. In addition, the routing of any arbitrary permutations on the networks with any integer k<2 is discussed. Further, by using the techniques developed here, the authors present an optimal O(log n) parallel algorithm for solving a set of linear equations with a nonsingular coefficient matrix when the arithmetic is over the finite field GF(p/sup t/).</p>
shuffle exchange networks; routing algorithm; linear permutations; permutation; linear-permutation-class; switching elements; positive integer number; optimal O(log n) parallel algorithm; nonsingular coefficient matrix; multiprocessor interconnection networks; parallel algorithms.

S. Huang, Y. Tseng, S. Tripathi and N. Chen, "An Efficient Routing Algorithm for Realizing Linear Permutations on p/sup t/-Shuffle-Exchange Networks," in IEEE Transactions on Computers, vol. 40, no. , pp. 1292-1298, 1991.
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