Lower bounds for synchronous networks and the advantage of local information

  • Rüdiger Reischuk
  • Meinolf Koshors
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 312)


For a natural, fairly general class of algorithms that solve a global problem like election in n-node m-link synchronous networks with local information we rigorously prove a lower bound Ω(m) for the number of messages that have to be exchanged among the processors. Without local information the lower bound becomes exactly m. This result matches (up to constant factors) the known upper bounds that hold even for asynchronous networks without local information. Further it is shown that relaxing any condition imposed on the algorithms one can design artificial protocols with message complexity O(n log n).


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [A80]
    D. Angluin, Local and Global Properties in Networks of Processors, Proc. 12. ACM Symp. on Theory of Computing, 1980, 82–93.Google Scholar
  2. [FL84]
    G. Frederickson, N. Lynch, The Impact of Synchronous Communication on the Problem of Electing a Leader on a Ring, Proc. 16. ACM Symp. on Theory of Computing 1984, 493–503.Google Scholar
  3. [GR80]
    R. Graham, B. Rothschild, J. Spencer, Ramsey Theory, J. Wiley, 1980.Google Scholar
  4. [GHS83]
    R. Gallager, P. Humblet, P. Spira, A Distributed Algorithm for Minimum-Weight Spanning Trees, ACM Tr. on Programming Languages and Systems 5, 1983, 66–77.CrossRefGoogle Scholar
  5. [KMZ84]
    E. Korach, S. Moran, S. Zaks, Tight Lower and Upper Bounds for Some Distributed Algorithms for a Complete Network of Processors, Proc.3.ACM Symp. on Principles of Distributed Computing, 1984, 199–207.Google Scholar
  6. [PKR84]
    J. Pachel, E. Korach, D. Rotem, A New Technique for Proving Lower Bounds for Distributed Maximum — Finding Algorithms, J.ACM 31, 1984, 905–918.CrossRefGoogle Scholar
  7. [V84]
    P. Vitanyi, Distributed Elections in an Archimedean Ring of Processors, Proc. 16. ACM Symp. on Theory of Computing 1984, 542–547.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Rüdiger Reischuk
    • 1
  • Meinolf Koshors
    • 1
  1. 1.Institut für Theoretische Informatik, TH DarmstadtDarmstadtWest-Germany

Personalised recommendations