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Self-stabilizing Cuts in Synchronous Networks

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Structural Information and Communication Complexity (SIROCCO 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5058))

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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.

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References

  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)

    Article  MathSciNet  Google Scholar 

  2. Dasgupta, A., Ghosh, S., Tixeuil, S.: Selfish stabilization. In: Stabilization, Safety, and Security of Distributed Systems (2006)

    Google Scholar 

  3. Diestel, R.: Graph Theory. Springer, Heidelberg (2005)

    MATH  Google Scholar 

  4. Dijkstra, E.W.: Self-stabilizing systems in spite of distributed control. Communications of the ACM 17(11), 643–644 (1974)

    Article  MATH  Google Scholar 

  5. Elkin, M.: Distributed approximation: a survey. SIGACT News 35(4), 40–57 (2004)

    Article  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  7. Ghosh, S., Karaata, M.H.: A self-stabilizing algorithm for coloring planar graphs. Distributed Computing 7(1), 55–59 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  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. 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. He, J., Yao, X.: A study of drift analysis for estimating computation time of evolutionary algorithms. Natural Computing 3(1), 21–35 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    Article  MATH  MathSciNet  Google Scholar 

  12. Hedetniemi, S.T., Jacobs, D.P., Srimani, P.K.: Linear time self-stabilizing colorings. Information Processing Letters 87(5), 251–255 (2003)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  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. Tovey, C.A.: Local improvement on discrete structures. In: Local search in combinatorial optimization, pp. 57–89. Princeton University Press, Princeton (1997)

    Google Scholar 

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Authors and Affiliations

  1. Dept. of CS, University of Paderborn, Paderborn, Germany

    Thomas Sauerwald

  2. Dept. of CS, Dortmund University of Technology, Dortmund, Germany

    Dirk Sudholt

Authors
  1. Thomas Sauerwald
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  2. Dirk Sudholt
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Alexander A. Shvartsman Pascal Felber

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© 2008 Springer-Verlag Berlin Heidelberg

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Sauerwald, T., Sudholt, D. (2008). Self-stabilizing Cuts in Synchronous Networks. In: Shvartsman, A.A., Felber, P. (eds) Structural Information and Communication Complexity. SIROCCO 2008. Lecture Notes in Computer Science, vol 5058. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69355-0_20

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  • DOI: https://doi.org/10.1007/978-3-540-69355-0_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-69326-0

  • Online ISBN: 978-3-540-69355-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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