An efficient routing algorithm for realizing linear permutations on pt-shuffle-exchange networks

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=kⁿ 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^t×p ^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^t)