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Brief Announcement: Stabilizing Consensus with the Power of Two Choices

  • Benjamin Doerr
  • Leslie Ann Goldberg
  • Lorenz Minder
  • Thomas Sauerwald
  • Christian Scheideler
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6343)

Abstract

Consensus problems occur in many contexts and have therefore been extensively studied in the past. In the original consensus problem, every process initially proposes a value, and the goal is to decide on a single value from all those proposed. We are studying a slight variant of the consensus problem called the stabilizing consensus problem [2]. In this problem, we do not require that each process irrevocably commits to a final value but that eventually they arrive at a common, stable value without necessarily being aware of that. This should work irrespective of the states in which the processes are starting. In other words, we are searching for a self-stabilizing algorithm for the consensus problem. Coming up with such an algorithm is easy without adversarial involvement, but we allow some adversary to continuously change the states of some of the nodes at will. Despite these state changes, we would like the processes to arrive quickly at a common value that will be preserved for as many time steps as possible (in a sense that almost all of the processes will store this value during that period of time). Interestingly, we will demonstrate that there is a simple algorithm for this problem that essentially needs logarithmic time and work with high probability to arrive at such a stable value, even if the adversary can perform arbitrary state changes, as long as it can only do so for a limited number of processes at a time.

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References

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    Angluin, D., Aspnes, J., Eisenstat, D.: A simple population protocol for fast robust approximate majority. In: Pelc, A. (ed.) DISC 2007. LNCS, vol. 4731, pp. 20–32. Springer, Heidelberg (2007)CrossRefGoogle Scholar
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    Angluin, D., Fischer, M., Jiang, H.: Stabilizing consensus in mobile networks. In: Gibbons, P.B., Abdelzaher, T., Aspnes, J., Rao, R. (eds.) DCOSS 2006. LNCS, vol. 4026, pp. 37–50. Springer, Heidelberg (2006)CrossRefGoogle Scholar
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    Doerr, B., Goldberg, L.A., Minder, L., Sauerwald, T., Scheideler, C.: Stabilizing consensus with the power of two choices. Technical report, University of Paderborn (2010), http://wwwcs.upb.de/cs/scheideler

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Benjamin Doerr
    • 1
  • Leslie Ann Goldberg
    • 2
  • Lorenz Minder
    • 3
  • Thomas Sauerwald
    • 4
  • Christian Scheideler
    • 5
  1. 1.Max-Planck Institute for Computer ScienceSaarbrücken
  2. 2.Department of Computer ScienceUniversity of Liverpool 
  3. 3.Computer Science DivisionUniversity of CaliforniaBerkeley
  4. 4.Simon Fraser UniversityBurnabyCanada
  5. 5.Department of Computer ScienceUniversity of Paderborn 

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