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Uniform dynamic self-stabilizing leader election

  • Shlomi Dolev
  • Amos Israeli
  • Shlomo Moran
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 579)

Abstract

A distributed system is selfstabilizing if it can be started in any possible global state. Once started the system regains its consistency by itself, without any kind of an outside intervention. The self-stabilization property makes the system tolerant to faults in which processors crash and then recover spontaneously in an arbitrary state. When the intermediate period in between one recovery and the next crash is long enough the system stabilizes. A distributed system is uniform if all processors with the same number of neighbors are identical. A distributed system is dynamic if it can tolerate addition or deletion of processors and links without reinitialization. In this work we present three dynamic, uniform, self-stabilizing protocols for leader election: The first protocol works on complete graphs. The second protocol works for systems with unbounded number of processor in which the size of the memory of a processor is unbounded. The third protocol works for systems whose communication graph has a bounded diameter; it uses a bounded amount of memory. We conclude this work by presenting a simple, uniform, self-stabilizing ranking protocol.

Keywords

Leader Election Atomic Step Communication Graph Leader Variable Good Block 
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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References

  1. [Ab-88]
    K. Abrahamson, “On Achieving Consensus Using a Shared Memory”, Proceedings of the Seventh Annual ACM Symposium on Principles of Distributed Computing, Toronto Canada, August 1988, pp. 291,302.Google Scholar
  2. [AG-90]
    A. Arora and M. Gouda: “Distributed Reset”, to appear in Proceedings of the Tenth Conference on Foundations of Software Technology and Theoretical Computer Science, Bangalore, India, December 1990.Google Scholar
  3. [AKY-90]
    Y. Afek, S. Kutten and M. Yung, “Memory-Efficient Self-Stabilization on General Networks”, it Proceedings of the 4th International Workshop on Distributed Algorithms, Bari Italy, September 1990.Google Scholar
  4. [BGW-87]
    G.M. Brown, M.G. Gouda, and C.L. Wu, “A Self-Stabilizing Token system”, Proc. of the Twentieth Annual Hawaii International Conference on System sciences 1987, pp. 218–223.Google Scholar
  5. [BP-88]
    J.E. Burns and J. Pachl, “Uniform Self-Stabilizing Rings”, Aegean Workshop On Computing, 1988, Lecture notes in computer science 319, pp. 391–400.Google Scholar
  6. [Bu-87]
    J.E. Burns, “Self-Stabilizing Rings without Demons”, Technical Report GIT-ICS-87/36, Georgia Institute of Technology.Google Scholar
  7. [CIL-87]
    B. Chor, A. Israeli, and M. Li, “On Processor Coordination Using Asynchronous Hardware”, Proc. of the Sixth Annual ACM Symposium on Principles of Distributed Computation, (1987), pp. 86–97.Google Scholar
  8. [Dij-74]
    E.W. Dijkstra, “Self-Stabilizing Systems in Spite of Distributed Control”, Communications of the ACM 17,11 1974, pp. 643–644.Google Scholar
  9. [DIM-90]
    S. Dolev, A. Israeli and S. Moran, “Self Stabilization of Dynamic Systems”, Proc. of the Ninth Annual ACM Symposium on Principles of Distributed Computation, Quebec City, August 1990, pp. 103–118.Google Scholar
  10. [DIM-91]
    S. Dolev, A. Israeli and S. Moran, “Resource Bounds for Self Stabilization Message Driven Protocols”, Proc. of the Tenth Annual ACM Symposium on Principles of Distributed Computation, Montreal, August 1991, pp. 281–294.Google Scholar
  11. [AE-91]
    E. Angnostou and R. El-Yaniv More on the Power of Random Walks: Uniform SelfStabilizing AlgorithmsGoogle Scholar
  12. [Ga-78]
    R. G. Gallagher, “Finding a leader in networks withe O(E)+O(NlogN) messages”, Internal Memo., M.I.T., Cambridge, Mass., 1978.Google Scholar
  13. [GHS-83]
    R.G. Gallager, P.M. Humblet and P.M. Spira, “A distributed algorithm for minimum weight spanning trees”, ACM Trans. Program. Lang. Sys. 5 1 (1983), pp. 66–77.Google Scholar
  14. [Hu-84]
    P. Humblet, “Selecting a leader in a clique in O(n log n messages. Inter. Memo., Laboratory for Information and Decision Systems, M.I.T, Cambridge, Mass., 1984.Google Scholar
  15. [IJ-90]
    A. Israeli and M. Jalfon, “Token Management Schemes and Random walks Yield Self Stabilizing Mutual Exclusion”, Proc. of the Ninth Annual ACM Symposium on Principles of Distributed Computation, Quebec City, August 1990, pp. 119–132.Google Scholar
  16. [IJ-90a]
    A. Israeli and M. Jalfon, “Self stabilizing Ring Orientation”, Proceedings of the 4th International Workshop on Distributed Algorithms, Bari Italy, September 1990.Google Scholar
  17. [IR-81]
    A. Itai and M. Rodeh, “Probabilistic Methods for Breaking Symmetry in Distributed Networks”, To appear in Information and Computation.Google Scholar
  18. [KKM-90]
    E. Korach, S. Kutten and S. Moran, “A Modular Technique for the Design of Efficient Distributed Leader Finding Algorithms”, ACM Trans. Program. Lang. Sys. 12, 1 (1990), 84–101.Google Scholar
  19. [KMZ-84]
    E. Korach, S. Moran and S.Zaks, “Tight lower and upper bounds for some distributed algorithms for complete network of processors”, Proc. of the 3rd Annual ACM Symposium on Principles od Distributed Computing (1984), pp. 199–207.Google Scholar
  20. [KP-89]
    S. Katz and K. J. Perry, “Self-stabilizing extensions for message-passing systems”, Proc. of the Ninth Annual ACM Symposium on Principles of Distributed Computation, Quebec City, August 1990, pp. 91–101.Google Scholar
  21. [Kr-79]
    H.S.M. Kruijer, “Self-stabilization (in spite of distributed control) in tree-structured systems”, Information Processing Letters 8,2 (1979), pp. 91–95.Google Scholar
  22. [La-86]
    L. Lamport, “The Mutual Exclusion Problem: Part II — Statement and Solutions”, Journal of the Association for Computing Machinery, Vol. 33 No. 2 (1986), pp. 327–348.Google Scholar
  23. [Pe-82]
    G. L. Peterson, “An O(n log n) unidirectional algorithm for the circular extrema problem”Google Scholar
  24. [SS-89]
    B. Schieber and M. Snir “Calling Names on Nameless Networks”, Proceedings of the Eights Annual Symposium on Principles of Distributed Computing, Edmonton, August 1989, pp. 319–328.Google Scholar
  25. [V-91]
    George Varghese, “Distributed Program Checking a Paradigm for Building Self-stabilizing Distributed Protocols”, To appear in FOCS-91.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Shlomi Dolev
    • 1
  • Amos Israeli
    • 2
  • Shlomo Moran
    • 3
  1. 1.Dept. of Computer ScienceTechnionIsrael
  2. 2.Dept. of Electrical EngineeringTechnionIsrael
  3. 3.Dept. of Computer ScienceTechnionIsrael

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