Acta Informatica

, Volume 47, Issue 5–6, pp 313–323 | Cite as

Randomization adaptive self-stabilization

Original Article

Abstract

We present a scheme to convert self-stabilizing algorithms that use randomization during and following convergence to self-stabilizing algorithms that use randomization only during convergence. We thus reduce the number of random bits from an infinite number to an expected bounded number. The scheme is applicable to the cases in which there exits a local predicate for each node, such that global consistency is implied by the union of the local predicates. We demonstrate our scheme over the token circulation algorithm of Herman (Infor Process Lett 35:63–67, 1990) and the recent constant time Byzantine self-stabilizing clock synchronization algorithm by Ben-Or, Dolev and Hoch (Proceedings of the 27th Annual ACM SIGACT-SIGOPS symposium on principles of distributed computing, (PODC), 2008). The application of our scheme results in the first constant time Byzantine self-stabilizing clock synchronization algorithm that eventually stops using random bits.

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References

  1. 1.
    Afek Y., Brown G.M.: Self-stabilization over unreliable communication media. Distrib. Comput. 7(1), 27–34 (1993)CrossRefGoogle Scholar
  2. 2.
    Afek Y., Dolev S.: Local stabilizer. J. Parallel Distrib. Comput. 62(5), 745–765 (2002)MATHCrossRefGoogle Scholar
  3. 3.
    Anagnostou, E., El-Yaniv, R., Hadzilacos, V.: Memory adaptive self-stabilizing protocols (extended abstract). In: Proceedings of the 6th International Workshop on Distributed Algorithms (WDAG 1992), pp. 203–220 (1992)Google Scholar
  4. 4.
    Ben-Or, M., Dolev, D., Hoch, E.N.: Fast self-stabilizing byzantine tolerant digital clock synchronization. In: Proceedings of the 27th Annual ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, (PODC) (2008)Google Scholar
  5. 5.
    Chandy K.M., Misra J.: The drinking philosophers problem. ACM Trans. Programming Languages Syst. 6(4), 632–646 (1984)CrossRefGoogle Scholar
  6. 6.
    Dolev S.: Self-Stabilization. MIT Press, Cambridge, MA (2000)MATHGoogle Scholar
  7. 7.
    Dolev S., Israeli A., Moran S.: Resource bounds for self-stabilizing message-driven protocols. SIAM J. Comput. 26(1), 273–290 (1997)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Dolev S., Schiller E.: Communication adaptive self-stabilizing group membership service. IEEE Trans. Parallel Distrib. Syst. 14(7), 709–720 (2003)CrossRefGoogle Scholar
  9. 9.
    Dolev, S., Welch, J.: Self-stabilizing clock synchronization in the presence of byzantine faults. In: Proceedings of the 2nd Workshop on Self-Stabilizing Systems, UNLV, May 1995. [Also in Journal of the ACM 51(5), 780–799 Sep (2004)]Google Scholar
  10. 10.
    Herman T.: Probabilistic self-stabilization. Infor. Process. Lett. 35, 63–67 (1990)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Katz S., Perry K.J.: Self-stabilizing extensions for message-passing systems. Distrib Comput 7(1), 17–26 (1993)CrossRefGoogle Scholar
  12. 12.
    Michael, R.O., Lehmann, D.: The advantages of free choice: a symmetric and fully distributed solution for the dining philosophers problem. In: A Classical Mind: Essays in Honor of C. A. R. Hoare, Prentice-Hall International Series In Computer Science, pp. 333–352 (1994)Google Scholar
  13. 13.
    Rao J.R.: Eventual determinism: using probabilistic means to achieve deterministic ends. Int. J. Parallel, Emergent Distrib. Syst. 8(1), 3–19 (1996)MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of Computer ScienceBen-Gurion University of the NegevBeer-ShevaIsrael

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