Asynchronous and Fully Self-stabilizing Time-Adaptive Majority Consensus

  • Janna Burman
  • Ted Herman
  • Shay Kutten
  • Boaz Patt-Shamir
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3974)


We study the scenario where a batch of transient faults hits an asynchronous distributed system by corrupting the state of some f nodes. We concentrate on the basic majority consensus problem, where nodes are required to agree on a common output value which is the input value of the majority of them. We give a fully self-stabilizing adaptive algorithm, i.e., the output value stabilizes in O(f) time at all nodes, for any unknown f. Moreover, a state stabilization occurs in time proportional to the (unknown) diameter of the network. Both upper bounds match known lower bounds to within a constant factor. Previous results (stated for a slightly less general problem called “persistent bit”) assumed the synchronous network model, and that f<n/2.


Stabilization Time Output Stabilization Transient Fault Parent Chain Faulty Node 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Afek, Y., Bremler-Barr, A.: Self-stabilizing unidirectional network algorithms by power-supply. In: The 8th SODA, pp. 111–120 (1997)Google Scholar
  2. 2.
    Afek, Y., Dolev, S.: Local stabilizer. In: Proceedings of the 5th Israel Symposium on Theory of Computing and Systems (June 1997)Google Scholar
  3. 3.
    Afek, Y., Kutten, S., Yung, M.: Memory-efficient self-stabilization on general networks. In: van Leeuwen, J., Santoro, N. (eds.) WDAG 1990. LNCS, vol. 486, pp. 15–28. Springer, Heidelberg (1991)CrossRefGoogle Scholar
  4. 4.
    Arora, A., Zhang, H.: LSRP: Local stabilization in shortest path routing. In: IEEE-IFIP DSN (2003)Google Scholar
  5. 5.
    Arora, A., Gouda, M.G.: Distributed reset. IEEE Transactions on Computers 43, 1026–1038 (1994)CrossRefMATHGoogle Scholar
  6. 6.
    Awerbuch, B., Kutten, S., Mansour, Y., Patt-Shamir, B., Varghese, G.: Time optimal self-stabilizing syncronization. In: The 25th STOC, pp. 652–661 (1993)Google Scholar
  7. 7.
    Awerbuch, B., Patt-Shamir, B., Varghese, G.: Self-stabilization by local checking and correction. In: The 32nd FOCS, pp. 268–277 (October 1991)Google Scholar
  8. 8.
    Beauquier, J., Hérault, T.: Fault Local Stabilization: the shortest path tree. In: SRDS 2002, pp. 62–69 (2002)Google Scholar
  9. 9.
    Bertsekas, D., Gallager, R.: Data Networks, 2nd edn. Prentice-Hall, Englewood Cliffs, New Jersey (1992)MATHGoogle Scholar
  10. 10.
    Boulinier, C., Petit, F., Villain, V.: When graph theory helps self-stabilization. In: The 23rd PODC, pp. 150–159 (2004)Google Scholar
  11. 11.
    Bremler-Barr, A., Afek, Y., Schwarz, S.: Improved BGP Convergence via Ghost Flushing. IEEE J. on Selected Areas in Communications 22, 1933–1948 (2004)CrossRefGoogle Scholar
  12. 12.
    Burman, J., Herman, T., Kutten, S., Patt-Shamir, B.: Asynchronous and Fully Self-Stabilizing Time-Adaptive Majority Consensus (extended version),
  13. 13.
    Couvreur, J.M., Francez, N., Gouda, M.: Asynchronous unison. In: The ICDCS 1992, pp. 486–493 (1992)Google Scholar
  14. 14.
    Dijkstra, E.W.: Self-stabilizing systems in spite of distributed control. Comm. ACM 17(11), 643–644 (1974)CrossRefMATHGoogle Scholar
  15. 15.
    Dolev, S., Gouda, M., Schneider, M.: Memory requirements for silent stabilization. In: The 15th PODC, pp. 27–34 (1996)Google Scholar
  16. 16.
    Dolev, S., Herman, T.: SuperStabilizing Protocols for Dynamic Distributed Systems. Chicago Journal of Theoretical Computer Science 4, 1–40 (1997)MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Dolev, S., Herman, T.: Parallel composition of stabilizing algorithms. In: WSS 1999: Proc. 1999 ICDCS Workshop on Self-Stabilizing Systems, pp. 25–32 (1999)Google Scholar
  18. 18.
    Dolev, S.: Self-Stabilization. MIT Press, Cambridge (2000)MATHGoogle Scholar
  19. 19.
    Dolev, S., Israeli, A., Moran, S.: Resource bounds for self stabilizing message driven protocols. In: The 10th PODC, pp. 281–294 (1991)Google Scholar
  20. 20.
    Fischer, M., Lynch, N.A., Paterson, M.S.: Impossibility of distributed consensus with one faulty process. J. ACM 32(2), 374–382 (1985)MathSciNetCrossRefMATHGoogle Scholar
  21. 21.
    Genolini, C., Tixeuil, S.: A lower bound on dynamic k-stabilization in asynchronous systems. In: SRDS 2002, pp. 211–221 (2002)Google Scholar
  22. 22.
    Herman, T.: Observations on time-adaptive self-stabilization. Technical Report TR 97-07Google Scholar
  23. 23.
    Herman, T.: Phase clocks for transient fault repair. IEEE Transactions on Parallel and Distributed Systems 11(10), 1048–1057 (2000)CrossRefGoogle Scholar
  24. 24.
    Ghosh, S., Gupta, A.: An exercise in fault-containment: self-stabilizing leader election. Inf. Proc. Let. 59, 281–288 (1996)MathSciNetMATHGoogle Scholar
  25. 25.
    Ghosh, S., Gupta, A., Herman, T., Pemmaraju, S.V.: Fault-containing self-stabilizing algorithms. In: The 15th PODC (1996)Google Scholar
  26. 26.
    Ghosh, S., Gupta, A., Pemmaraju, S.V.: A fault-containing self-stabilizing algorithm for spanning trees. J. Computing and Information 2, 322–338 (1996)Google Scholar
  27. 27.
    Katz, S., Perry, K.: Self-stabilizing extensions for message-passing systems. In: The 10th PODC (1990)Google Scholar
  28. 28.
    Kutten, S., Patt-Shamir, B.: Asynchronous time-adaptive self stabilization. In: The 17th PODC, p. 319 (1998)Google Scholar
  29. 29.
    Kutten, S., Patt-Shamir, B.: Time-Adaptive self-stabilization. In: The 16th PODC, pp. 149–158 (1997)Google Scholar
  30. 30.
    Kutten, S., Peleg, D.: Fault-local distributed mending. In: The 14th PODC (1995)Google Scholar
  31. 31.
    Parlati, G., Yung, M.: Non-exploratory self-stabilization for constant-space symmetry-breaking. In: van Leeuwen, J. (ed.) ESA 1994. LNCS, vol. 855, pp. 26–28. Springer, Heidelberg (1994)Google Scholar
  32. 32.
    Zhang, H., Arora, A., Liu, Z.: A Stability-Oriented Approach to Improving BGP Convergence. In: SRDS 2004, pp. 90–99 (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Janna Burman
    • 1
  • Ted Herman
    • 2
  • Shay Kutten
    • 1
  • Boaz Patt-Shamir
    • 3
  1. 1.Dept. of Industrial Engineering & Management, TechnionHaifaIsrael
  2. 2.Dept. of Computer ScienceUniversity of IowaIowa CityUSA
  3. 3.Dept. of Electrical EngineeringTel-Aviv UniversityTel AvivIsrael

Personalised recommendations