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Rearrangeable Three-Stage Interconnection Networks and Their Routing Properties
May 1993 (vol. 42 no. 5)
pp. 559-567

A rearrangeable network is an interconnection network which can achieve all possible permutations of its inputs' connections to its outputs. One class of rearrangeable networks, which have been studied are Clos three-stage networks. Earlier procedures to route such networks rapidly require an excessive amount of hardware, either in the network itself or in the device required to compute the routing. A class of rearrangeable three-stage networks which is both compact and which can be routed quickly is introduced, along with a routing scheme. Switches are added to the network so as to reduce the interdependence between the switch settings, allowing faster routing while only moderately increasing network complexity. A network with O(Nlog/sup 1.5/N) hardware and O(log/sup 1.5/N) depth is derived from O(log/sup 2.5/N) switch setup time.

[1] M. Ajtai, J. Komlos, and E. Szemeredi, "AnO(nlogn) sorting network," inProc. 15th ACM Symp. Theory Comput., 1983, pp. 1-9.
[2] S. Andresen, "The looping algorithm extended to base 2trearrangeable switching networks,"IEEE Trans. Commun., vol. COM-25, no. 10, pp. 1057-1063, Oct. 1977.
[3] K. E. Batcher, "Sorting networks and their applications," inProc. 1968 Spring Joint Comput. Conf., pp. 307-314.
[4] V. E. Benes,Mathematical Theory of Connecting Networks and Telephone Traffic. New York: Academic, 1965.
[5] C.-Y. Chin and K. Hwang, "Packet switching networks for multiprocessor and data flow computers,"IEEE Trans. Comput., vol. C-33, pp. 991-1003, May 1975.
[6] Y. C. Chow, R. D. Dixon, T-Y Feng, and C-L. Wu, "Routing techniques for rearrangeable interconnection networks," inProc. Interconnection Networks, Computer Society Pub., 1980, pp. 64-69.
[7] C. Clos, "A study of non-blocking switching networks,"Bell Syst. Tech. J., pp. 406-424, Mar. 1953.
[8] D. M. Koppelman and A. Y. Oruç"A self-routing permutation network," inProc., 1989 Int. Conf. Parallel Processing, Aug. 1989, pp. 288-295.
[9] G. F. Lev, N. Pippenger, and L. Valiant, "A fast parallel algorithm for routing in permutation networks,"IEEE Trans. Comput., vol. C-30, no. 2, pp. 93-100, Feb. 1981.
[10] D. Nassimi and S. Sahni, "Parallel algorithms to set up the Benes permutation network,"IEEE Trans. Comput., vol. C-31, no. 2, pp. 148-154, Feb. 1982.
[11] D. Nassimi and S. Sahni, "Parallel permutation and sorting algorithms and a new generalized connection network,"J. ACM, vol. 29, no. 3, pp. 642-667, 1982.
[12] M. E. Kopache and E. P. Glinert, "C2: A mixed textual/graphical environment for C," inProc. IEEE Workshop Visual Languages. 1988, pp. 231-238.
[13] H. S. Stone, "Parallel processing with the perfect shuffle,"IEEE Trans. Comput., vol. C-20, no. 2, pp. 153-161, Feb. 1971.
[14] C. D. Thompson, "Generalized interconnection networks for parallel processor intercommunication,"IEEE Trans. Comput., vol. C-27, pp. 1119-1125, Dec. 1978.
[15] C. L. Wu and T. Feng, "Universality of the shuffle-exchange network,"IEEE Trans. Comput., vol. C-30, pp. 324-331, May 1981.

Index Terms:
rearrangeable network; interconnection network; permutations; Clos three-stage networks; routing scheme; switch settings; network complexity; computational complexity; multiprocessor interconnection networks.
Citation:
B.G. Douglass, "Rearrangeable Three-Stage Interconnection Networks and Their Routing Properties," IEEE Transactions on Computers, vol. 42, no. 5, pp. 559-567, May 1993, doi:10.1109/12.223675
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