Mathematical systems theory

, Volume 27, Issue 5, pp 431–452 | Cite as

Designing broadcasting algorithms in the postal model for message-passing systems

  • A. Bar-Noy
  • S. KipnisEmail author


In many distributed-memory parallel computers and high-speed communication networks, the exact structure of the underlying communication network may be ignored. These systems assume that the network creates a complete communication graph between the processors, in which passing messages is associated with communication latencies. In this paper we explore the impact of communication latencies on the design of broadcasting algorithms for fully connected message-passing systems. For this purpose, we introduce thepostal model that incorporates a communication latency parameter λ ≥ 1. This parameter measures the inverse of the ratio between the time it takes an originator of a message to send the message and the time that passes until the recipient of the message receives it. We present an optimal algorithm for broadcasting one message in systems withn processors and communication latency λ, the running time of which is Θ((λ logn)/log(λ + 1)). For broadcastingm ≥ 1 messages, we first examine several generalizations of the algorithm for broadcasting one message and then analyze a family of broadcasting algorithms based on degree-d trees. All the algorithms described in this paper are practical event-driven algorithms that preserve the order of messages.


Communication Network Optimal Algorithm Computational Mathematic Parallel Computer Passing Message 
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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  1. [1]
    A. Bar-Noy and S. Kipnis, Designing broadcasting algorithms in the postal model for message-passing systems,Proceedings of the 4th Annual Symposium on Parallel Algorithms and Architectures, June 1992, pp. 13–22. Also appeared as IBM Research Report RC-17429, November 1991.Google Scholar
  2. [2]
    A. Bar-Noy and S. Kipnis, Multiple message broadcasting in the postal model,Proceedings of the 7th International Parallel Processing Symposium, Newport Beach, CA, April 1993. Also appeared as IBM Research Report RC-18230, August 1992.Google Scholar
  3. [3]
    D. P. Bertsekas and J. N. Tsitsiklis,Parallel and Distributed Computation: Numerical Methods, Prentice-Hall, Englewood Cliffs, New Jersey, 1989.Google Scholar
  4. [4]
    I. Cidon and I. Gopal, PARIS: an approach to integrated high-speed private networks,International Journal of Digital and Analog Cabled Systems, Vol. 1, No. 2, April–June 1988, pp. 77–85.Google Scholar
  5. [5]
    I. Cidon, I. Gopal, and S. Kutten, New models and algorithms for future networks,Proceedings of the 7th Annual Symposium on Principles of Distributed Computing, August 1988, pp. 75–89.Google Scholar
  6. [6]
    I. Cidon, I. Gopal, and S. Kutten, Optimal computation of global sensitive functions in fast networks, inDistributed Algorithms, J. van Leeuwen and N. Santoro, eds., Lecture Notes in Computer Science, Vol. 486, Springer-Verlag, New York, 1990, pp. 185–191.Google Scholar
  7. [7]
    D. Clark, B. Davie, D. Farber, I. Gopal, B. Kadaba, D. Sincoskie, J. Smith, and D. Tennenhouse, The AURORA gigabit testbed,Computer Networks and ISDN, 1991.Google Scholar
  8. [8]
    D. Culler, R. Karp, D. Patterson, A. Sahay, K. E. Schauser, E. Santos, R. Subramonian, and T. von Eicken, LogP: towards a realistic model of parallel computation,Proceedings of the 4th SIGPLAN Symposium on Principles and Practices of Parallel Programming, San Diego, CA, May 1993.Google Scholar
  9. [9]
    W. J. Dally, A. Chien, S. Fiske, W. Horwat, J. Keen, M. Larivee, R. Letton, P. Nuth, S. Wills, P. Carrick, and G. Fyler, The J-Machine: a fine-grain concurrent computer,Information Processing 89, Elsevier Science, Amsterdam, 1989, pp. 1147–1153.Google Scholar
  10. [10]
    G. Fox, M. Johnson, G. Lyzenga, S. Otto, I Salmon, and D. Walker,Solving Problems on Concurrent Processors, Vol. I, Prentice-Hall, Englewood Cliffs, New Jersey, 1988.Google Scholar
  11. [11]
    S. M. Hedetniemi, S. T. Hedetniemi, and A. L. Liestman, A survey of gossiping and broadcasting hi communication networks,Networks, Vol. 18, No. 4, 1988, pp. 319–349.Google Scholar
  12. [12]
    C. E. Leiserson, Z. S. Abuhamdeh, D. C. Douglas, C. R. Feynman, M. N. Ganmukhi, J. V Hill, W. D. Hills, B. C. Kuszmaul, M. A. St. Pierre, D. S. Wells, M. C. Wong, S.-W. Yang, and R. Zak, The network architecture of the Connection Machine CM-5,Proceedings of the 4th Annual Symposium on Parallel Algorithms and Architectures, June 1992, pp. 272–285.Google Scholar
  13. [13]
    P. D. Mackenzie, A lower bound for order preserving broadcast in the postal model, manuscript, University of Texas at Austin, December 1992.Google Scholar
  14. [14]
    S. Report and R. Special, Gigabit network testbeds, Special Report,IEEE Computer Magazine, Vol. 23, No. 9, 1990, pp. 77–80.Google Scholar
  15. [15]
    J. S. Turner and L. F. Wyatt, A packet network architecture for integrated services,GLOBECOM 83, 1983, pp. 2.1.1–2.1.6.Google Scholar
  16. [16]
    C. B. Stunkel, D. G. Shea, B. Abali, M. M. Denneau, P. H. Hochschild, D. J. Joseph, B. J. Nathanson, M. Tsao, and P. R. Varker, Architecture and implementation of Vulcan,Proceedings of the 8th International Parallel Processing Symposium, Cancun, Mexico, April 1994, pp. 268–274.Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1994

Authors and Affiliations

  1. 1.Computer Sciences DepartmentIBM T. J. Watson Research CenterYorktown HeightsUSA

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