Self-stabilizing Leader Election in Population Protocols over Arbitrary Communication Graphs

  • Joffroy Beauquier
  • Peva Blanchard
  • Janna Burman
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8304)

Abstract

This paper considers the fundamental problem of self-stabilizing leader election (\(\mathcal{SSLE}\)) in the model of population protocols. In this model, an unknown number of asynchronous, anonymous and finite state mobile agents interact in pairs over a given communication graph. \(\mathcal{SSLE}\) has been shown to be impossible in the original model. This impossibility can been circumvented by a modular technique augmenting the system with an oracle - an external module abstracting the added assumption about the system. Fischer and Jiang have proposed solutions to \(\mathcal{SSLE}\), for complete communication graphs and rings, using an oracle Ω?, called the eventual leader detector. In this work, we present a solution for arbitrary graphs, using a composition of two copies of Ω?. We also prove that the difficulty comes from the requirement of self-stabilization, by giving a solution without oracle for arbitrary graphs, when an uniform initialization is allowed. Finally, we prove that there is no self-stabilizing implementation of Ω? using \(\mathcal{SSLE}\), in a sense we define precisely.

Keywords

leader election self-stabilization population protocols global fairness oracles 

References

  1. 1.
    Angluin, D.: Local and global properties in networks of processors. In: 12th Symposium on the Theory of Computing, pp. 82–93. ACM (1980)Google Scholar
  2. 2.
    Angluin, D., Aspnes, J., Diamadi, Z., Fischer, M.J., Peralta, R.: Computation in networks of passively mobile finite-state sensors. In: PODC, pp. 290–299 (2004)Google Scholar
  3. 3.
    Angluin, D., Aspnes, J., Diamadi, Z., Fischer, M.J., Peralta, R.: Computation in networks of passively mobile finite-state sensors. Distributed Computing 18(4), 235–253 (2006)CrossRefMATHGoogle Scholar
  4. 4.
    Angluin, D., Aspnes, J., Fischer, M.J., Jiang, H.: Self-stabilizing population protocols. ACM Trans. Auton. Adapt. Syst. 3(4) (2008)Google Scholar
  5. 5.
    Beauquier, J., Blanchard, P., Burman, J.: Self-stabilizing leader election in population protocols over arbitrary communication graphs. Technical report, INRIA (2013), http://hal.archives-ouvertes.fr/hal-00867287
  6. 6.
    Beauquier, J., Blanchard, P., Burman, J., Denysyuk, O.: Oracles for self-stabilizing leader election in population protocols. Technical report, INRIA (2013), http://hal.archives-ouvertes.fr/hal-00839759
  7. 7.
    Boldi, P., Shammah, S., Vigna, S., Codenotti, B., Gemmell, P., Simon, J.: Symmetry breaking in anonymous networks: Characterizations. In: ISTCS, pp. 16–26 (1996)Google Scholar
  8. 8.
    Cai, S., Izumi, T., Wada, K.: How to prove impossibility under global fairness: On space complexity of self-stabilizing leader election on a population protocol model. Theory Comput. Syst. 50(3), 433–445 (2012)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Canepa, D., Potop-Butucaru, M.G.: Self-stabilizing tiny interaction protocols. In: WRAS, pp. 10:1–10:6 (2010)Google Scholar
  10. 10.
    Chandra, T.D., Hadzilacos, V., Toueg, S.: The weakest failure detector for solving consensus. J. ACM 43(4), 685–722 (1996)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Chandra, T.D., Toueg, S.: Unreliable failure detectors for reliable distributed systems. J. ACM 43(2), 225–267 (1996)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Charron-Bost, B., Hutle, M., Widder, J.: In search of lost time. Inf. Process. Lett. 110(21), 928–933 (2010)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Dijkstra, E.W.: Self-stabilizing systems in spite of distributed control. Commun. of the ACM 17(11), 643–644 (1974)CrossRefMATHGoogle Scholar
  14. 14.
    Fischer, M., Jiang, H.: Self-stabilizing leader election in networks of finite-state anonymous agents. In: OPODIS, pp. 395–409 (2006)Google Scholar
  15. 15.
    Fischer, M.H., Lynch, N.A., Paterson, M.S.: Impossibility of consensus with one faulty process. Journal of the ACM 32(2), 374–382 (1985)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Michail, O., Chatzigiannakis, I., Spirakis, P.G.: Mediated population protocols. Theor. Comput. Sci. 412(22), 2434–2450 (2011)MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Michail, O., Chatzigiannakis, I., Spirakis, P.G.: Terminating population protocols via some minimal global knowledge assumptions. In: SSS, pp. 77–89 (2012)Google Scholar
  18. 18.
    Mizoguchi, R., Ono, H., Kijima, S., Yamashita, M.: On space complexity of self-stabilizing leader election in mediated population protocol. Distributed Computing 25(6), 451–460 (2012)CrossRefMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Joffroy Beauquier
    • 1
  • Peva Blanchard
    • 2
  • Janna Burman
    • 1
  1. 1.LRI, Paris-South 11 UniversityOrsayFrance
  2. 2.LRIOrsay CedexFrance

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