Gossiping and broadcasting versus computing functions in networks

  • Martin Dietzfelbinger
Boolean Functions
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1200)

Abstract

The fundamental assumption in the classical theory of gossiping, broadcasting, and accumulation in networks is that atomic pieces of information are communicated in messages that consist of a set of such pieces. The communication mode in synchronous multiprocessor networks that are to compute a function does not fit this model. We show that, under certain assumptions about the way processors may communicate (“predictable reception”), computing an arbitrary n-ary function that has a “critical input” and distributing the result to all processors on an n-processor network takes at least as long as performing gossiping in the network graph. A similar relation exists between computing functions with the output appearing at only one processor and the complexity of broadcasting. Our methods can also be applied to extend known lower bounds for broadcasting a bit on EREW PRAMs to the much more general (randomized) distributed memory machines (DMMs).

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References

  1. 1.
    P. Beame, M. Kutyłowski, and M. Kik, Information Broadcasting by exclusive-read PRAMs, Parallel Processing Letters 1 & 2 (1994) 159–169.CrossRefGoogle Scholar
  2. 2.
    G. Belting, Untere Schranken für die Berechnung von Booleschen Funktionen in vollständigen Prozessornetzwerken im Telefon-und Telegraf-Modus, Diplomarbeit, Universität-Gesamthochschule-Paderborn, Paderborn, 1994.Google Scholar
  3. 3.
    S. Cook, C. Dwork, and R. Reischuk, Upper and lower time bounds for parallel random access machines without simultaneous writes, SIAM J. Comput. 15 (1986) 87–97.CrossRefGoogle Scholar
  4. 4.
    M. Dietzfelbinger, Gossiping and broadcasting versus computing functions in networks, ECCC (http://www.eccc.uni-trier.de/eccc/), Report TR96-052, 1996.Google Scholar
  5. 5.
    M. Dietzfelbinger, M. Kutyłowski, and R. Reischuk, Exact time bounds for computing Boolean functions on PRAMs without simultaneous writes, in: Proc. 2nd Annual ACM Symp. on Parallel Algorithms and Architectures, 1990, pp. 125–135.Google Scholar
  6. 6.
    M. Dietzfelbinger, M. Kutyłowski, and R. Reischuk, Exact lower bounds for computing Boolean functions on CREW PRAMs, J. Comput. Syst. Sci. 48 (1994) 1231–254.Google Scholar
  7. 7.
    M. Dietzfelbinger and F. Meyer auf der Heide, Simple, efficient shared memory simulations, in: Proc. 5th ACM Symp. on Parallel Algorithms and Architectures, 1993, pp. 110–118.Google Scholar
  8. 8.
    S. Even and B. Monien, On the number of rounds necessary to disseminate information, in: Proc. ACM Symp. on Parallel Algorithms and Architectures, 1989, pp. 318–327.Google Scholar
  9. 9.
    F. Fich, The complexity of computation on the parallel random access machine, in J. H. Reif (ed.), Synthesis of Parallel Computation, Morgan Kaufmann, San Mateo, 1994, pp. 843–899.Google Scholar
  10. 10.
    P. Fraigniaud and E. Lazard, Methods and problems of communication in usual networks, Discrete Applied Math. 53 (1994) 79–134.CrossRefGoogle Scholar
  11. 11.
    L. A. Goldberg, M. Jerrum, T. Leighton, and S. Rao, A doubly logarithmic communication algorithm for the completely connected optical communication parallel computer, in: Proc. 5th Annual ACM Symp. on Parallel Algorithms and Architectures, 1993, pp. 300–309.Google Scholar
  12. 12.
    L. A. Goldberg, Y. Matias, and S. Rao, An optical simulation of shared memory, in: Proc. 6th Annual ACM Symp. on Parallel Algorithms and Architectures, 1994, pp. 257–267.Google Scholar
  13. 13.
    S. M. Hedetniemi, S. T. Hedetniemi, and A. L. Liestman, A survey of gossiping and broadcasting in communication networks, Networks 18 (1986) 319–349.Google Scholar
  14. 14.
    I. Höltring, Broadcast und Gossip in parallelen Netzwerken, Diplomarbeit, Universität-Gesamthochschule-Paderborn, Paderborn, 1994.Google Scholar
  15. 15.
    J. Hromkovič, C.-D. Jeschke, and B. Monien, Optimal algorithms for dissemination of information in some interconnection networks, Algorithmica 10 (1993) 24–40.CrossRefGoogle Scholar
  16. 16.
    J. Hromkovič, R. Klasing, B. Monien, and R. Peine, Dissemination of information in interconnection networks (broadcasting & gossiping), in: D.-Z. Du and D. F. Hsu (eds.), Combinatorial Network Theory, Kluwer Academic Publishers, Amsterdam, 1996, pp. 125–212.Google Scholar
  17. 17.
    R. M. Karp and V. Ramachandran, Parallel algorithms for shared-memory machines, in J. van Leeuwen (ed.), Handbook of Theoretical Computer Science, Vol. A, Algorithms and Complexity, Elsevier, Amsterdam, 1990, pp. 869–941.Google Scholar
  18. 18.
    D. W. Krumme, G. Cybenko, and K. N. Venkatamaran, Gossiping in minimal time, SIAM J. Comput. 21 (1992) 111–139.CrossRefMathSciNetGoogle Scholar
  19. 19.
    R. Labahn and I. Warnke, Quick gossiping by multi-telegraphs, in: R. Bodendiek and R. Henn (eds.), Topics in Combinatorics and Graph Theory, Physica-Verlag, Heidelberg, 1990, pp. 451–458.Google Scholar
  20. 20.
    F. Meyer auf der Heide, C. Scheideler, and V. Stemann, Exploiting storage redundancy to speed up randomized shared memory simulations, in: E. W. Mayr and C. Puech (eds.), Proc. 12th Annual Symposium on Theoretical Aspects of Computer Science (STACS 95), Lecture Notes in Computer Science 900, Springer, Berlin, 1995, pp. 267–278.Google Scholar
  21. 21.
    D. Richards and A. L. Liestman, Generalizations of broadcasting and gossiping, Networks 18 (1988) 125–138.Google Scholar
  22. 22.
    V. S. Sunderam and P. Winkler, Fast information sharing in a complete network, Discrete Applied Math. 42 (1991) 75–86.CrossRefGoogle Scholar
  23. 23.
    G. Tel, Introduction to Distributed Algorithms, Cambridge University Press, Cambridge, 1994.Google Scholar
  24. 24.
    U. Vishkin and A. Wigderson, Trade-offs between depth and width in parallel computation, SIAM J. Comput. 14 (1985) 303–314.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • Martin Dietzfelbinger
    • 1
  1. 1.Fachbereich InformatikUniversität DortmundDortmundGermany

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