New upperbounds for decentralized extrema-finding in a ring of processors

  • H. L. Bodlaender
  • J. van Leeuwen
Contributed Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 210)

Abstract

We show that decentralized extrema-finding ("election") is more efficient in bidirectional rings than in unidirectional rings of processors, by exhibiting a (non-probabilistic) algorithm for distributed extrema-finding in bidirectional rings that requires fewer messages on the average than any such algorithm for unidirectional rings.

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4. References

  1. [1]
    Bodlaender, H.L. and J. van Leeuwen, New upperbounds for decentralized extrema-finding in a ring of processors, Tech. Rep. RUU-CS-85-15, Dept. of Computer Science, University of Utrecht, Utrecht, 1985.Google Scholar
  2. [2]
    Burns, J.E., A formal model for message passing systems, Techn. Rep. 91, Computer Sci. Dept., Indiana University, Bloomington, IN., 1980.Google Scholar
  3. [3]
    Chandler, K.N., The distribution and frequency of record values, J. Roy. Stat. Soc., Series B, 14(1952) 220–228.Google Scholar
  4. [4]
    Chang, E., and R. Roberts, An improved algorithm for decentralized extremafinding in circular configurations of processes, C. ACM 22 (1979) 281–283.Google Scholar
  5. [5]
    David, F.N., and D.E. Barton, Combinatorial chance, Charles Griffin & Comp., London, 1962.Google Scholar
  6. [6]
    Dolev, D., M. Klawe, and M. Rodeh, An O(nlogn) unidirectional distributed algorithm for extrema finding in a circle, J. Algorithm 3 (1982) 245–260.Google Scholar
  7. [7]
    Foster, F.G., and A. Stuart, Distribution-free tests in time-series based on the breaking of records, J. Roy. Stat. Soc., Series B, 16(1954) 1–13.Google Scholar
  8. [8]
    Franklin, W.R., On an improved algorithm for decentralized extrema finding in circular configurations of processors, C.ACM 25(1982) 336–337.Google Scholar
  9. [9]
    Gallager, R.G., P.A. Humblet, and P.M. Spira, A distributed algorithm for minimum-weight spanning trees, ACM Trans. Prog. Lang. and Syst. 5(1983) 66–77.Google Scholar
  10. [10]
    Haghighi-Talab, D., and C. Wright, On the distribution of records in a finite sequence of observations, with an application to a road traffic problem, J. Appl. Prob. 10(1973) 556–571.Google Scholar
  11. [11]
    Hirschberg, D.S., and J.B. Sinclair, Decentralized extrema-finding in circular configurations of processors, C.ACM 23(1980) 627–628.Google Scholar
  12. [12]
    Korach, E., D.Rotem, and N. Santoro, A probabilistic algorithm for decentralized extrema-finding in a circular configuration of processors, Res. Rep. CS-81-19, Dept. of Computer Science, Univ. of Waterloo, Waterloo, 1981.Google Scholar
  13. [13]
    LeLann, G., Distributed systems-towards a formal approach, in: B. Gilchrist (ed.), Information Processing 77 (IFIP), North-Holland Publ. Comp., Amsterdam, 1977, pp. 155–160.Google Scholar
  14. [14]
    Pachl, J., E. Korach, and D. Rotem, A technique for proving lower bounds for distributed maximum-finding algorithms, Proc. 14th ACM Symp. Theory of Computing, 1982, pp.378–382.Google Scholar
  15. [15]
    Peterson, G.L., An O(nlogn) unidirectional algorithm for the circular extrema problem, ACM Trans. Prog. Lang. and Syst. 4(1982) 758–762.Google Scholar
  16. [16]
    Renyi, A., Egy megfigyeléssorozat kiemelkedö elemeiröl (On the extreme elements of observations), MTA III. Oszt. Közl. 12(1962) 105–121.Google Scholar
  17. [17]
    Santoro, N., E. Korach, and D. Rotem, Decentralized extrema-finding in circular configurations of processors: and improved algorithm, Congr. Numer. 34(1982) 401–412.Google Scholar
  18. [18]
    van Leeuwen, J., and R.B. Tan, An improved upperbound for distributed election in bidirectional rings of processors, Tech. Rep. RUU-CS-85-23, Dept. of Computer Science, University of Utrecht, Utrecht, 1985.Google Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • H. L. Bodlaender
    • 1
  • J. van Leeuwen
    • 1
  1. 1.Department of Computer ScienceUniversity of UtrechtUtrechtthe Netherlands

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