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An Efficient Routing Algorithm for Realizing Linear Permutations on p/sup t/-Shuffle-Exchange Networks
November 1991 (vol. 40 no. 11)
pp. 1292-1298

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/).

[1] K. E. Batcher, "Sorting networks and their applications," inProc. AFIPS Conf., 1968, pp. 307-314.
[2] R. Cole and J. Hopcroft, "On edge coloring bipartite graphs,"SIAM J. Comput., vol. 11, no. 3, pp. 540-546, Aug. 1982.
[3] L. Csanky, "Fast parallel matrix inversion algorithm,"SIAM J. Comput., vol. 5, no. 4, pp. 618-623, Dec. 1976.
[4] T. Etzion and A. Lempel, "An efficient algorithm for generating linear transformations in a shuffle-exchange network,"SIAM J. Comput., vol. 15, no. 1, pp. 216-221, Feb. 1986.
[5] P. M. Flanders, "A unified approach to a class of data movements on an array processor,"IEEE Trans. Comput., vol. C-31, pp. 809-819, Sept. 1982.
[6] H. N. Gabow, "Using Euler partitions to edge color bipartite multigraphs,"J. Comput. Inform. Sci., vol. 5, no. 4, pp. 345-355, 1976.
[7] G. Birkhoff and S. Maclane,A Survey of Modern Algebra. New York: Macmillan, 1977, chs. 8 and 13.
[8] K. Hoffman and R. Kunze,Linear Algebra. Englewood Cliffs, NJ: Prentice-Hall, 1971, pp. 28-58.
[9] S.-T. Huang and S. K. Tripathi, "Finite state model and compatibility theory: New analysis tools for permutation networks,"IEEE Trans. Comput., vol. C-35, no. 7, pp. 591-601, July 1986.
[10] S. T. Huang and S. K. Tripathi, "Self-routing technique in perfect-shuffle networks using control tags,"IEEE Trans. Comput., vol. C-37, pp. 251-256, Feb. 1988.
[11] D. H. Lawrie, "Access and alignment of data in an array processor,"IEEE Trans. Comput., vol. C-24, pp. 1145-1155, Dec. 1975.
[12] J. Lefant, "Parallel permutations of data: A Benes network control algorithm for frequently used permutations,"IEEE Trans. Comput., vol. C-27, pp. 637-647, July 1978.
[13] G. F. Lev, N. Pippenger, and L. G. Valiant, "A fast parallel algorithm for routing in permutation networks,"IEEE Trans. Comput., vol. C-30, pp. 93-100, Feb. 1981.
[14] N. Linial and M. Tarsi, "Interpolation between bases and the shuffle exchange network," Tech. Rep., Dep. Math., Hebrew Univ., Jerusalem, Israel.
[15] D. Nassimi and S. Sahni, "An optimal routing algorithm for meshconnected parallel computer,"J. ACM, vol. 27, pp. 6-29, Jan. 1980.
[16] D. S. Parker, "Notes on shuffle/exchange-type switching networks,"IEEE Trans. Comput., vol. C-29, pp. 213-221, Mar. 1980.
[17] M. C. Pease, "The indirect binary n-cube microprocessor array,"IEEE Trans. Comput., vol. C-26, pp. 458-473, May 1977.
[18] Y. Shiloach and U. Vishkin, "AnO(logn) parallel connectivity algorithm,"J. Algorithm, vol. 3, pp. 57-67, 1982.
[19] D. Steinberg, "Invariant properties of the shuffle-exchange and a simplified cost-effective version of the Omega network,"IEEE Trans. Comput., vol. C-32, pp. 444-450, May 1983.
[20] H. S. Stone, "Parallel processing with the perfect shuffle,"IEEE Trans. Comput., vol. C-20, pp. 153-161, Feb. 1971.
[21] A. Varma and C.S. Raghavendra, "Rearrangeability of multistage shuffle/exchange networks," inProc. Int. Conf. Comput. Arch., 1987, pp. 154-162.
[22] C. Wu and T. Feng, "The universality of the shuffle-exchange network,"IEEE Trans. Comput., vol. C-30, pp. 324-331, May 1981.

Index Terms:
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.
Shing-Tsaan Huang, S.K. Tripathi, Nian-Shing Chen, Yu-Chee Tseng, "An Efficient Routing Algorithm for Realizing Linear Permutations on p/sup t/-Shuffle-Exchange Networks," IEEE Transactions on Computers, vol. 40, no. 11, pp. 1292-1298, Nov. 1991, doi:10.1109/12.102836
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