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Embedding Properties of Reconfigurable Partitionable Optical Networks

  • Ted H. Szymanski
  • S. Thomas Obenaus
Chapter

Abstract

This chapter describes the embedding properties of some emerging reconfigurable and partitionable optical networks, and motivates and formalizes several combinatorial optimization problems associated with embeddings in these networks. In particular, the embedding properties of a reconfigurable multichannel free-space optical backplane called the “HyperPlane” will be described. The networks to be embedded can be conventional point-to-point networks which are modeled as graphs G(V, E), or bus-based networks which are modeled as hypergraphs H(V, E). By partitioning the backplane optical channels appropriately, the optical backplane can be dynamically reconfigured to embed arbitrary networks in real time. The optical backplane can thus provide terabits of low latency bandwidth for message-passing multiprocessors based upon graphs, and shared memory multiprocessors based upon broadcast busses. It is also shown that partitionable optical networks exhibit a significant improvement in performance over non-partitionable optical networks.

Keywords

Field Programmable Gate Array Optical Network Optical Channel Optical Interconnection Data Flow Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    A. Barak and E. Schenfeld. Embedding classical communication topologies in the scalable OPAM architecture. IEEE Transactions on Parallel and Distributed Systems, 7 (9): 962–978, Sept. 1996.Google Scholar
  2. [2]
    C. Berge. Hypergraphs. North-Holland Mathematical Library, Amsterdam, 1989.zbMATHGoogle Scholar
  3. [3]
    J.-C. Bermond, J. Bond, and S. Djelloul. Dense bus networks of diameter 2. Research Report 94–46, CNRS, Université de Nice Sophia-Antipolis, Aug. 1994.Google Scholar
  4. [4]
    J.-C. Bermond, J. Bond, and J.-F. Saclé. Large hypergraphs of diameter 1. In Bollobas, editor, Graph Theory and Combinatorics. Academic Press, 1984.Google Scholar
  5. [5]
    P. Berthomé and A. Ferreira. Improved embeddings in POPS networks through stack-graph models. In Third International Workshop on Massively Parallel Processing using Optical Interconnections, pages 130–136. IEEE CS Press, Oct. 1996.CrossRefGoogle Scholar
  6. [6]
    J. Bhasker and S. Sahni. Optimal linear arrangement of circuit components. Journal of VLSI and Computer Systems, pages 87–109, 1987.Google Scholar
  7. [7]
    J. A. Bondy and U. S. R. Murphy. Graph Theory with Apllications. North Holland, 1984.Google Scholar
  8. [8]
    H. Bourdin, A. Ferreira, and K. Marcus. A comparative study of one-to-many WDM lightwave interconmnection networks for multiprocessors. In Second International Workshop on Massively Parallel Processing using Optical Interconnections,pages 257–253, San Antonio (USA), Oct. 1995. IEEE Press.Google Scholar
  9. [9]
    S. D. Brown, R. J. Francis, J. Rose, and Z. G. Vranesic. Field Programmable Gate Arrays. Kluwer Academic Publishers, 1992.Google Scholar
  10. [10]
    Canadian Institute for Telecommunications Research. Research program 199697, photonic devices and systems, Aug. 1996. (http://www.citr.ee.mcgill.ca).Google Scholar
  11. [11]
    J. P. Cohoon and S. Sahni. Heuristics for backplane ordering. Journal of VLSI and Computer Systems, pages 37–60, 1987.Google Scholar
  12. [12]
    Cray Research Inc. Cray T3D system architectural overview, Sept. 1993.Google Scholar
  13. [13]
    P. Desai. Embeddings of a cray T3D supercomputer into the optical backplane. Microelectronics and Computer Systems (MACS) Laboratory, McGill University, Montreal, Quebec, Canada.Google Scholar
  14. [14]
    P. W. Dowd. Wavelength division multiple access channel hypercube processor interconnection. IEEE Transactions on Computers, 41 (10): 1223–1241, Oct. 1992.CrossRefGoogle Scholar
  15. [15]
    E. E. E. Frietman. Opto-electronic processing and networking: A design study. Delft University of Technology Printing Office, 1995.Google Scholar
  16. [16]
    M. Garey and D. Johnson. Computers and Intractability. A guide to the theory of NP-completeness. W. Freeman and Compagny, New York, 1979.Google Scholar
  17. [17]
    G. Gravenstreter and R. G. Melhem. Embedding rings and meshes in partitioned optical passive star networks. In Second International Workshop on Massively Parallel Processing using Optical Interconnections,pages 220–227, San Antonio (USA), Oct. 1995. IEEE Press.Google Scholar
  18. [18]
    Z. Guo, R. G. Melhem, R. W. Hall, D. M. Chiarulli, and S. P. Levitan. Pipelined communications in optically interconnected arrays. Journal of Parallel and Distributed Computing, 12 (3): 269–282, July 1991.CrossRefGoogle Scholar
  19. [19]
    J. H. Ha and T. M. Pinkston. The SPEED cache coherence protocol for an optical multi-access interconnect architecture. In Second International Workshop on Massively Parallel Processing using Optical Interconnections, pages 98–107, San Antonio (USA), Oct. 1995. IEEE Press.Google Scholar
  20. [20]
    H. S. Hinton and T. H. Szymanski. Intelligent optical backplanes. In Second International Workshop on Massively Parallel Processing using Optical Interconnections, pages 133–143, San Antonio (USA), Oct. 1995. IEEE Press.Google Scholar
  21. [21]
    J. Kilian, S. Kipnis, and C. E. Leiserson. The organization of permutation architectures with bused interconnections. IEEE Transactions on Computers, 39 (11): 1346–1358, Nov. 1990.ADSCrossRefGoogle Scholar
  22. [22]
    R. K. Kostuck, T. J. Kim, D. Ramsey, T.-H. Oh, and R. Boye. Connection cube and interleaved optical backplane for a multiprocessor data bus. In Second International Workshop on Massively Parallel Processing using Optical Interconnections, pages 144–151, San Antonio (USA), Oct. 1995. IEEE Press.Google Scholar
  23. [23]
    B. Krishnamurthy and M. S. Krishnamoorthy. The difficulty of funding good embeddings of program graphs onto the OPAM architecture. In Second International Workshop on Massively Parallel Processing using Optical Interconnections, pages 124–129, San Antonio (USA), Oct. 1995. IEEE Press.Google Scholar
  24. [24]
    F. T. Leighton. Introduction to Parallel Algorithms: Arrays, Trees, Hypercubes. Morgan-Kaufmann, San Mateo, CA, 1991.Google Scholar
  25. [25]
    Y. Li, S. B. Rao, I. Redmond, and T. Wing. Free-space WDMA optical interconnects using mesh-connected bus topology. In Proc. Int. Conf. Optical Computing (OC’94), pages 153–156, Edinburgh, 1994. Institute of Physics Publishing.Google Scholar
  26. [26]
    G. Liu, K. Y. Lee, and H. F. Jordan. n-dimensional processor arrays with optical buses. In Second International Workshop on Massively Parallel Processing using Optical Interconnections, pages 116–123, San Antonio (USA), Oct. 1995. IEEE Press.Google Scholar
  27. [27]
    L. M. Mackenzie, M. Ould-Khaoua, R. J. Sutherland, and T. Kelly. Cobra: A high-performance interconnection for large multicomputers. Computing Science Research Report 1991/R19, University of Glasgow, Oct. 1991.Google Scholar
  28. [28]
    T. S. Obenaus. Topology of a high speed free-space photonic network. Master’s thesis, Depts. Elec. Eng. and Computer Science, McGill University,.Google Scholar
  29. [29]
    T. S. Obenaus and T. H. Szymanski. Embedding star graphs into optical meshes without bends. Submitted.Google Scholar
  30. [30]
    I. Redmond and E. Schenfeld. A distributed reconfigurable free-space optical interconnection network for massively parallel processing architectures. In Proc. Int. Conf. Optical Computing, pages 215–218, Edinburgh, Aug. 1994. Institute of Physics Publishing.Google Scholar
  31. [31]
    D. R. Rolston, D. V. Plant, T. H. Szymanski, H. S. Hinton, M. H. Ayliffe, D. N. Kabal, A. V. Krishnamoorthy, K. W. Goosen, J. A. Walker, B. Tseng, S. P. Hui, J. C. Cunningham, and W. Y. Jan. A hybrid-SEED smart pixel array for a four-stage intelligent optical backplane demonstrator. Journal of Quantum Electronics, pages 97–105, Apr. 1996. Special Issue on Smart Pixels.Google Scholar
  32. [32]
    I. Scherson. Orthogonal graphs for a class of interconnection networks. IEEE Transactions on Parallel and Distributed Systems, 2 (1): 3–19, Jan. 1991.CrossRefGoogle Scholar
  33. [33]
    H. J. Siegel. The theory underlying the partitioning of permutation networks. IEEE Transactions on Computers, 29 (9): 791–800, 1980.zbMATHCrossRefGoogle Scholar
  34. [34]
    Q. F. Stout. Mesh-connected computers with broadcasting. IEEE Transactions on Computers, 32 (9): 826–830, Sept. 1983.zbMATHCrossRefGoogle Scholar
  35. [35]
    T. Szymanski. Graph-theoretic models for photonic networks. In I. Scherson, editor, Proceedings of New Frontiers: A Workshop on Future Directions of Massively Parallel Processing, pages 85–96. IEEE Computer Society, IEEE Press, Oct. 1992.CrossRefGoogle Scholar
  36. [36]
    T. H. Szymanski. Hypermeshes–optical interconnection networks for parallel computing. Journal of Parallel and Distributed Computing, 26: 1–23, Apr. 1995.zbMATHCrossRefGoogle Scholar
  37. [37]
    T. H. Szymanski and H. S. Hinton. Reconfigurable intelligent optical backplane for parallel computing and communications. Applied Optics, pages 1253–1268, Mar. 1996. Special Issue on Optical Computing.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1998

Authors and Affiliations

  • Ted H. Szymanski
    • 1
  • S. Thomas Obenaus
    • 1
  1. 1.Departments of Electrical Engineering and Computer ScienceMcGill UniversityMontrealCanada

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