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Nonblocking Routing Properties of Clos Networks

Chapter
Part of the Network Theory and Applications book series (NETA, volume 5)

Abstract

By a connecting system we shall mean a physical communication system consisting of (i) a set of terminals, (ii) control units which process requests for connections between pairs of terminals, and (iii) a connecting network through which the connections are effected. The connecting network is an arrangement of arrays of crosspoints (called crossbars or switches) and transmission links through which certain terminals can be connected together in many combinations.

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References

  1. [1]
    V.E. Benes. Mathematical Theory of Connecting Networks and Telephone Traffic. Mathematics in Science and Engineering, Vol. 17. Academic Press, New York, 1965.zbMATHGoogle Scholar
  2. [2]
    S.-P. Chung and K.W. Ross. On nonblocking multirate interconnection networks. SIAM Journal on Computing, 20: 726–736, 1991.MathSciNetzbMATHCrossRefGoogle Scholar
  3. [3]
    C. Clos. A study of non-blocking switching networks. The Bell System Technical Journal, 32: 406–424, 1953.Google Scholar
  4. [4]
    D. de Werra. Balanced schedules. INFOR. Canadian Journal of Operational Research and Information Processing, 9: 230–237, 1971.Google Scholar
  5. [5]
    D.Z. Du, P.C. Fishburn, B. Gao, and F.K. Hwang. Wide-sense non-blocking for 3-stage Clos networks. Technical report, Department of Computer Science, University of Minnesota, 1995.Google Scholar
  6. [6]
    D.Z. Du, B. Gao, F.K. Hwang, and J.H. Kim. On multirate rearrange-able Clos networks. SIAM Journal of Computing, 28: 463–470, 1999.MathSciNetCrossRefGoogle Scholar
  7. [7]
    D.Z. Du, X.D. Hu, G.-H. Lin, H.Z. Shi, and S.X. Gao. On wide-sense nonblocking in 1-rate environment for 3-stage Clos networks. Technical report, Institute of Applied Mathematics, Chinese Academy of Sciences, 1997.Google Scholar
  8. [8]
    A.M. Duguid. Structural properties of switching networks. Progr. rept. BTL-7, Brown Univ., 1959.Google Scholar
  9. [9]
    P.C. Fishburn, F.K. Hwang, D.Z. Du, and B. Gao. On 1-rate wide-sense nonblocking for 3-stage Clos networks. Discrete Applied Mathematics, 78: 75–87, 1997.MathSciNetzbMATHCrossRefGoogle Scholar
  10. [10]
    B. Gao and F.K. Hwang. Wide-sense nonblocking for multirate 3-stage Clos networks. Theoretical Computer Sciences, 182: 171–182, 1997.MathSciNetzbMATHCrossRefGoogle Scholar
  11. [11]
    A. Jajszczyk. On nonblocking switching networks composed of digital symmetrical matrices. IEEE Transactions on Communications, COM 31: 2–9, 1983.zbMATHCrossRefGoogle Scholar
  12. [12]
    D.S. Kim and D.Z. Du. Multirate broadcast switching networks non-blocking in a wide sense. In Advances in Switching Networks, DIMACS Series in Discrete Mathematics and Theoretical Computer Science 42, pages 59–74. American Mathematics Society, Providence, RI, 1998.Google Scholar
  13. [13]
    D.S. Kim and D.Z. Du. Multirate multicast switching networks. In Proceedings of the Fourth Annual International Computing and Combinatorics Conference (COCOON’98), LNCS, pages 219–228, 1998.Google Scholar
  14. [14]
    G.-H. Lin, D.-Z. Du, X.-D. Hu, and G. Xue. On rearrangeability of multirate Clos networks. SIAM Journal on Computing, 28: 1225–1231, 1999.MathSciNetzbMATHCrossRefGoogle Scholar
  15. [15]
    G.-H. Lin, D.Z. Du, W. Wu, and K. Yoo. On 3-rate rearrangeability of Clos networks. In Advances in Switching Networks, DIMACS Series in Discrete Mathematics and Theoretical Computer Science 42, pages 315–333. American Mathematics Society, Providence, RI, 1998.Google Scholar
  16. [16]
    G.-H. Lin, D.S. Kim, and D.Z. Du. Strictly nonblocking multirate multi-cast Clos networks. In Proceedings of the 10th International Conference on Parallel and Distributed Computing and Systems, pages 417–420, 1998.Google Scholar
  17. [17]
    R. Melen and J.S. Turner. Nonblocking multirate networks. SIAM Journal on Computing, 18: 301–313, 1989.MathSciNetzbMATHCrossRefGoogle Scholar
  18. [18]
    G. Niestegge. Nonblocking multirate switching networks. In M. Bonatti and M. Decina, editors, Traffic Engineering for ISDN Designing and Planning, Elsevier, Amsterdam, 1988.Google Scholar
  19. [19]
    M.C. Paull. Reswitching of connection networks. The Bell System Technical Journal, 41: 833–855, 1962.Google Scholar
  20. [20]
    D. Slepian. Two problems on a particular crossbar switching network. Unpublished manuscript, 1952.Google Scholar
  21. [21]
    Y. Yang and G.M. Masson. Nonblocking broadcast switching networks. IEEE Transactions on Computers, 40: 1005–1015, 1991.CrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  1. 1.Department of Computing and SoftwareMcMaster UniversityHamiltonCanada

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