Loosely-Stabilizing Leader Election in Population Protocol Model

  • Yuichi Sudo
  • Junya Nakamura
  • Yukiko Yamauchi
  • Fukuhito Ooshita
  • Hirotsugu Kakugawa
  • Toshimitsu Masuzawa
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5869)

Abstract

A self-stabilizing protocol guarantees that starting from an arbitrary initial configuration, a system eventually comes to satisfy its specification and keeps the specification forever. Although self-stabilizing protocols show excellent fault-tolerance against any transient faults (e.g. memory crash), designing self-stabilizing protocols is difficult and, what is worse, might be impossible due to the severe requirements. To circumvent the difficulty and impossibility, we introduce a novel notion of loose-stabilization, that relaxes the closure requirement of self-stabilization; starting from an arbitrary configuration, a system comes to satisfy its specification in a relatively short time, and it keeps the specification for a long time, though not forever. To show effectiveness and feasibility of this new concept, we present a probabilistic loosely-stabilizing leader election protocol in the Probabilistic Population Protocol (PPP) model of complete networks. Starting from any configuration, the protocol elects a unique leader within O(nNlogn) expected steps and keeps the unique leader for Ω(NeN) expected steps, where n is the network size (not known to the protocol) and N is a known upper bound of n. This result proves that introduction of the loose-stabilization circumvents the already-known impossibility result; the self-stabilizing leader election problem in the PPP model of complete networks cannot be solved without the knowledge of the exact network size.

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References

  1. 1.
    Angluin, D., Aspnes, J., Chan, M., Fischer, M.J., Jiang, H., Peralta, R.: Stably computable properties of network graphs. In: Prasanna, V.K., Iyengar, S.S., Spirakis, P.G., Welsh, M. (eds.) DCOSS 2005. LNCS, vol. 3560, pp. 63–74. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  2. 2.
    Angluin, D.: Computation in networks of passively mobile finite-state sensors. Distributed Computing 18(4), 235–253 (2006)CrossRefMATHGoogle Scholar
  3. 3.
    Angluin, D., Aspnes, J., Eisenstat, D.: Fast Computation by Population Protocols with a Leader. In: Proceedings of Distributed Computing, 20th International Symposium, pp. 61–75 (2006)Google Scholar
  4. 4.
    Angluin, D., Aspnes, J., Fischer, M.J., Jiang, H.: Self-stabilizing Population Protocols. In: Proceedings of Principles of Distributed Systems, pp. 103–117 (2006)Google Scholar
  5. 5.
    Cai, S., Izumi, T., Wada, K.: Space Complexity of Self-Stabilizing Leader Election in Passively-Mobile Anonymous Agents (to be submitted)Google Scholar
  6. 6.
    Devismes, S., Tixeuil, S., Yamashita, M.: Weak vs. self vs. probabilistic stabilization. In: Proceedings of the IEEE International Conference on Distributed Computing Systems (ICDCS 2008), pp. 681–688 (2008)Google Scholar
  7. 7.
    Dijkstra, E.W.: Self-stabilizing systems in spite of distributed control. Communications of the ACM 17(11), 643–644 (1974)CrossRefMATHGoogle Scholar
  8. 8.
    Fischer, M.J., Jiang, H.: Self-stabilizing leader election in networks of finite-state anonymous agents. In: Shvartsman, M.M.A.A. (ed.) OPODIS 2006. LNCS, vol. 4305, pp. 395–409. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  9. 9.
    Gouda, M.G.: The Theory of Weak Stabilization. In: Datta, A.K., Herman, T. (eds.) WSS 2001. LNCS, vol. 2194, pp. 114–123. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  10. 10.
    Israeli, A., Jalfon, M.: Token management schemes and random walks yield self-stabilizing mutual exclusion. In: Proceedings of the ninth annual ACM symposium on Principles of distributed computing, pp. 119–131. ACM Press, New York (1990)CrossRefGoogle Scholar
  11. 11.
    Lin, J.C., Huang, T.C., Yang, C.Z., Mou, N.: Quasi-self-stabilization of a distributed system assuming read/write atomicity. Computers and Mathematics with Applications 57(2), 184–194 (2009)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Mitzenmacher, M., Upfal, E.: Probability and Computing: Randomized Algorithms and Probabilistic Analysis. Cambridge University Press, Cambridge (2005)CrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Yuichi Sudo
    • 1
  • Junya Nakamura
    • 1
  • Yukiko Yamauchi
    • 2
  • Fukuhito Ooshita
    • 1
  • Hirotsugu Kakugawa
    • 1
  • Toshimitsu Masuzawa
    • 1
  1. 1.Graduate School of Information Science and TechnologyOsaka UniversityOsakaJapan
  2. 2.Graduate School of Information ScienceNara Institute of Science and TechnologyIkomaJapan

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