Self-stabilizing Cuts in Synchronous Networks

  • Thomas Sauerwald
  • Dirk Sudholt
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5058)

Abstract

Consider a synchronized distributed system where each node can only observe the state of its neighbors. Such a system is called self-stabilizing if it reaches a stable global state in a finite number of rounds. Allowing two different states for each node induces a cut in the network graph. In each round, every node decides whether it is (locally) satisfied with the current cut. Afterwards all unsatisfied nodes change sides independently with a fixed probability p. Using different notions of satisfaction enables the computation of maximal and minimal cuts, respectively. We analyze the expected time until such cuts are reached on several graph classes and consider the impact of the parameter p and the initial cut.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Chen, B., Matsumoto, M., Wang, J., Zhang, Z., Zhang, J.: A short proof of Nash-Williams’ theorem for the arboricity of a graph. Graphs and Combinatorics 10(1), 27–28 (1994)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Dasgupta, A., Ghosh, S., Tixeuil, S.: Selfish stabilization. In: Stabilization, Safety, and Security of Distributed Systems (2006)Google Scholar
  3. 3.
    Diestel, R.: Graph Theory. Springer, Heidelberg (2005)MATHGoogle Scholar
  4. 4.
    Dijkstra, E.W.: Self-stabilizing systems in spite of distributed control. Communications of the ACM 17(11), 643–644 (1974)MATHCrossRefGoogle Scholar
  5. 5.
    Elkin, M.: Distributed approximation: a survey. SIGACT News 35(4), 40–57 (2004)CrossRefGoogle Scholar
  6. 6.
    Gairing, M., Goddard, W., Hedetniemi, S.T., Kristiansen, P., McRae, A.A.: Distance-two information in self-stabilizing algorithms. Parallel Processing Letters 14(3-4), 387–398 (2004)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Ghosh, S., Karaata, M.H.: A self-stabilizing algorithm for coloring planar graphs. Distributed Computing 7(1), 55–59 (1993)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Goddard, W., Hedetniemi, S.T., Jacobs, D.P., Srimani, P.K.: Self-stabilizing protocols for maximal matching and maximal independent sets for ad hoc networks. In: 17th International Parallel and Distributed Processing Symposium (IPDPS 2003), p. 162. IEEE Computer Society, Los Alamitos (2003)Google Scholar
  9. 9.
    Gradinariu, M., Tixeuil, S.: Self-stabilizing vertex coloration and arbitrary graphs. In: Procedings of the 4th International Conference on Principles of Distributed Systems, OPODIS 2000, pp. 55–70 (2000)Google Scholar
  10. 10.
    He, J., Yao, X.: A study of drift analysis for estimating computation time of evolutionary algorithms. Natural Computing 3(1), 21–35 (2004)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Hedetniemi, S.T., Jacobs, D.P., Srimani, P.K.: Maximal matching stabilizes in time O(m). Information Processing Letters 80(5), 221–223 (2001)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Hedetniemi, S.T., Jacobs, D.P., Srimani, P.K.: Linear time self-stabilizing colorings. Information Processing Letters 87(5), 251–255 (2003)CrossRefMathSciNetGoogle Scholar
  13. 13.
    Huang, S.-T., Hung, S.-S., Tzeng, C.-H.: Self-stabilizing coloration in anonymous planar networks. Information Processing Letters 95(1), 307–312 (2005)CrossRefMathSciNetGoogle Scholar
  14. 14.
    Kosowski, A., Kuszner, Ł.: Self-stabilizing algorithms for graph coloring with improved performance guarantees. In: Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., Żurada, J.M. (eds.) ICAISC 2006. LNCS (LNAI), vol. 4029, pp. 1150–1159. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  15. 15.
    Manne, F., Mjelde, M., Pilard, L., Tixeuil, S.: A new self-stabilizing maximal matching algorithm. In: Prencipe, G., Zaks, S. (eds.) SIROCCO 2007. LNCS, vol. 4474, pp. 96–108. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  16. 16.
    Sauerwald, T., Sudholt, D.: Self-stabilizing cuts in synchronous networks. Technical Report CI-244/08, Collaborative Research Center 531, Technische Universität Dortmund (2008)Google Scholar
  17. 17.
    Tovey, C.A.: Local improvement on discrete structures. In: Local search in combinatorial optimization, pp. 57–89. Princeton University Press, Princeton (1997)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Thomas Sauerwald
    • 1
  • Dirk Sudholt
    • 2
  1. 1.Dept. of CSUniversity of PaderbornPaderbornGermany
  2. 2.Dept. of CSDortmund University of TechnologyDortmundGermany

Personalised recommendations