Random leaders and random spanning trees

  • Judit Bar-Ilan
  • Dror Zernik
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 392)


The problem of distributively constructing a minimum spanning tree has been thoroughly studied. The root of this spanning tree is often elected as a leader, and then centralized algorithms are run in the distributed system. If, however, we have fault tolerance in mind, selecting a random spanning tree and a random leader are more desirable. If we manage to select a random tree, the probability that a bad channel will disconnect some nodes from the random tree is relatively small. Otherwise, a small number of predetermined edges will greatly effect the system's behavior.

In this paper we present an algorithm for choosing a random leader (RL), and distributed random spanning tree algorithms (RST), where random means, that each spanning tree in the underlying graph has the same probability of being selected. We give optimal algorithms for the complete graph and the ring. We also describe an RST algorithm for the general graph, and discuss the relation between RST and RL algorithms.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [AG]
    Afek, Y. and Gafni, E., Time and Message Bounds for Election in Synchronous and Asynchronous Complete Networks, PODC 1985, pp 199–207.Google Scholar
  2. [AHU]
    Aho, V. A., Hopcroft, J.E. and Ullman, J.D., The Design and Analysis of Computer Algorithms, Addison-Wesley, 1974.Google Scholar
  3. [A]
    Awerbuch, B., Linear Time Distributed Algorithms for Minimum Spanning Trees, leader election, counting and related problems, 19th STOC, 1987, pp. 230–240.Google Scholar
  4. [B]
    Broder, A. Z., Generating Random Spanning Trees, To appear in 30th FOCS, 1989.Google Scholar
  5. [Bi]
    Biggs, N., Algebraic Graph Theory Google Scholar
  6. [BK]
    Broder, A. Z. and Karlyn, A. R., Bounds on Cover Time 29th FOCS, 1988.Google Scholar
  7. [Bu]
    Burns, J. E., A Formal Model for Message Passing Systems, TR-91, Indiana University, 1980.Google Scholar
  8. [E]
    Even, S., Graph Algorithms, Maryland, Computer Science Press, 1979.Google Scholar
  9. [FL]
    Fredrickson, G. N. and Lynch N. A., The Impact of Synchronous Communication On the Problem of Electing a Leader in a Ring, STOC84, pp. 493–503.Google Scholar
  10. [Ga]
    Gafni, E., Improvements in the Time Complexity of Two Message-Optimal Election Algorithms, PODC85, pp 175–184.Google Scholar
  11. [GHS]
    Gallager, R. G., Humblet, P. A. and Spira, P. M., A Distributed Algorithm for Minimum Weight Spanning Trees, ACM Trans. Program. Lang. Syst., vol 5. pp. 66–77, January 1983.Google Scholar
  12. [G]
    Guenoche, A., Random Spanning Trees, J. Algorithm, vol 4, pp. 214–220, 1983.Google Scholar
  13. [H]
    Harary, F., Graph Theory Addison-Wesley, 1972.Google Scholar
  14. [KS]
    Kemeny, J.G and Snell, J.L., Finite Markov Chains Lect. Notes in Math, vol 69.Google Scholar
  15. [MVV]
    Mulmuley, K., Vazirani, U. V. and Vazirani, V. J., Matching is as Easy as Matrix Inversion, 19th STOC, 1987, pp. 345–354.Google Scholar
  16. [QN]
    Quinn, M. J. and Narsingh Deo, Parallel Graph Algorithms, Computing Surveys, vol 16. No. 3, September 1984, pp 319–348.Google Scholar
  17. [V]
    Vitanyi, P., Distributed Election in an Archimedian Ring of Processors, STOC84, pp 542–547.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Judit Bar-Ilan
    • 1
  • Dror Zernik
    • 1
  1. 1.Department of Computer ScienceHebrew UniversityJerusalemIsrael

Personalised recommendations