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A Self-stabilizing Algorithm for Finding a Minimal K-Dominating Set in General Networks

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Data and Knowledge Engineering (ICDKE 2012)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 7696))

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Abstract

Since the publication of Dijkstra’s pioneering paper, a lot of self-stabilizing algorithms for computing dominating sets have been proposed in the literature. However, there is no self-stabilizing algorithm for the minimal k-dominating set (MKDS) in arbitrary graphs that works under a distributed daemon. The proposed algorithms for the minimal k-dominating set (MKDS) either work for trees (Kamei and Kakugawa [16]) or find a minimal 2-dominating set (Huang et al. [14,15]). In this paper, we propose a self-stabilizing algorithm for the minimal k-dominating set (MKDS) under a central daemon model when operating in any general network. We further prove that the worst case convergence time of the algorithm from any arbitrary initial state is O(n 2) steps where n is the number of nodes in the network.

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References

  1. Beauquier, J., Datta, A.K., Gradinariu, M., Magniette, F.: Self-Stabilizing Local Mutual Exclusion and Daemon Refinement. In: Herlihy, M.P. (ed.) DISC 2000. LNCS, vol. 1914, pp. 223–237. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  2. Dijkstra, E.W.: Self-stabilizing Systems in Spite of Distributed Control. ACM. Commun. 17(11), 643–644 (1974)

    Article  MATH  Google Scholar 

  3. Dijkstra, E.W.: A Simple Fixpoint Argument Without the Restriction to Continuity. J. Acta. Inf. 23(1), 1–7 (1986)

    Article  MathSciNet  Google Scholar 

  4. Dolev, S.: Self-Stabilization. MIT Press, Cambridge (2000)

    MATH  Google Scholar 

  5. Gairing, M., Hedetniemi, S.T., Kristiansen, P., McRae, A.A.: Self-Stabilizing Algorithms for {k}-Domination. In: Huang, S.-T., Herman, T. (eds.) SSS 2003. LNCS, vol. 2704, pp. 49–60. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  6. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman, New York (1979)

    MATH  Google Scholar 

  7. Goddard, W., Hedetniemi, S.T., Jacobs, D.P., Srimani, P.K.: A self-stabilizing distributed algorithm for minimal total domination in an arbitrary system grap. In: 17th International Symposium on Parallel and Distributed Processing, pp. 485–488. IEEE Press, Nice (2003)

    Google Scholar 

  8. Goddard, W., Hedetniemi, S.T., Jacobs, D.P., Srimani, P.K., Xu, Z.: Self-stabilizing graph protocols. Parallel Processing Letters 18(1), 189–199 (2008)

    Article  MathSciNet  Google Scholar 

  9. Guellati, N., Kheddouci, H.: A survey on self-stabilizing algorithms for independence, domination, coloring, and matching in graphs. Journal of Parallel and Distributed Computing 70(4), 406–415 (2010)

    Article  MATH  Google Scholar 

  10. Haynes, T.W., Hedetniemi, S.T., Slater, P.J.: Domination in Graphs: Advanced Topics. Marcel Dekker, New York (1998)

    MATH  Google Scholar 

  11. Haynes, T.W., Hedetniemi, S.T., Slater, P.J.: Fundamentals of Domination in Graphs. Marcel Dekker, New York (1998)

    Google Scholar 

  12. Hedetniemi, S.M., Hedetniemi, S.T., Jacobs, D.P., Srimani, P.K.: Self-stabilizing algorithms for minimal dominating sets and maximal independent sets. Computer Mathematics and Applications 46(5-6), 805–811 (2003)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  14. Huang, T.C., Chen, C.Y., Wang, C.P.: A Linear-Time Self-Stabilizing Algorithm for the Minimal 2-Dominating Set Problem in General Networks. Inf. Sci. Eng. 24(1), 175–187 (2008)

    MathSciNet  Google Scholar 

  15. Huang, T.C., Lin, J.C., Chen, C.Y., Wang, C.P.: A self-stabilizing algorithm for finding a minimal 2-dominating set assuming the distributed demon model. Computers and Mathematics with Applications 54(3), 350–356 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  16. Kamei, S., Kakugawa, H.: A self-stabilizing algorithm for the distributed minimal k-redundant dominating set problem in tree network. In: 4th International Conference on Parallel and Distributed Computing, Applications and Technologies, pp. 720–724. IEEE Press, Chengdu (2003)

    Google Scholar 

  17. Manne, F., Mjelde, M., Pilard, L., Tixeuil, S.: A New Self-Stabilizing Maximal Matching Algorithm. Theoretical Computer Science. 410(14), 1336–1345 (2008)

    Article  MathSciNet  Google Scholar 

  18. Nesterenko, M., Arora, A.: Stabilization-Preserving Atomicity Refinement. Journal of Parallel and Distributed Computing 62(5), 766–791 (2002)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Maths and Computing, University of Southern Queensland, QLD, 4350, Australia

    Guangyuan Wang, Hua Wang, Xiaohui Tao & Ji Zhang

Authors
  1. Guangyuan Wang
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  2. Hua Wang
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  3. Xiaohui Tao
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  4. Ji Zhang
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Editor information

Editors and Affiliations

  1. School of Information Technology, Deakin University, Melbourne Burwood Campus, 221 Burwood Highway, 3125, Burwood, VIC, Australia

    Yang Xiang

  2. Media Distribution, Telstra Corporation Limited, 21/35 Collins St, 3000, Melbourne, VIC, Australia

    Mukaddim Pathan

  3. Department of Mathematics and Computing, The University of Southern Queensland, Toowoomba, QLD, Australia

    Xiaohui Tao

  4. Department of Mathematics and Computing, The University of Southern Queensland, Toowoomba, QLD, Australia

    Hua Wang

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© 2012 Springer-Verlag Berlin Heidelberg

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Wang, G., Wang, H., Tao, X., Zhang, J. (2012). A Self-stabilizing Algorithm for Finding a Minimal K-Dominating Set in General Networks. In: Xiang, Y., Pathan, M., Tao, X., Wang, H. (eds) Data and Knowledge Engineering. ICDKE 2012. Lecture Notes in Computer Science, vol 7696. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34679-8_8

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  • DOI: https://doi.org/10.1007/978-3-642-34679-8_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-34678-1

  • Online ISBN: 978-3-642-34679-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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