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Game-Theoretic Approach to Self-stabilizing Minimal Independent Dominating Sets

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Internet and Distributed Computing Systems (IDCS 2018)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 11226))

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Abstract

An independent dominating set (IDS) is a set of vertices in a graph that ensures both independence and domination. The former property asserts that no vertices in the set are adjacent to each other while the latter demands that every vertex not in the set is adjacent to at least one vertex in the IDS. We extended two prior game designs, one for independent set and the other for dominating set, to three IDS game designs where players independently determine whether they should be in or out of the set based on their own interests. Regardless of the game play sequence, the result is a minimal IDS (i.e., no proper subset of the result is also an IDS). We turned the designs into three self-stabilizing distributed algorithms that always end up with an IDS regardless of the initial configurations. Simulation results show that all the game designs produce relatively small IDSs with reasonable convergence rate in representative network topologies.

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References

  1. Barabási, A.L., Albert, R.: Emergence of scaling in random networks. Science 286, 509–512 (1999)

    Article  MathSciNet  Google Scholar 

  2. Cohen, J., Dasgupta, A., Ghosh, S., Tixeuil, S.: An exercise in selfish stabilization. ACM Trans. Auton. Adapt. Syst. 3(4), 15:1–15:12 (2008)

    Article  Google Scholar 

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

    Article  Google Scholar 

  4. Dolev, S., Gouda, M.G., Schneider, M.: Memory requirements for silent stabilization. Acta Informatica 36, 447–462 (1999)

    Article  MathSciNet  Google Scholar 

  5. Erdös, P., Rényi, A.: On random graphs I. Publ. Math. Debr. 6, 290–297 (1959)

    MATH  Google Scholar 

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

    MATH  Google Scholar 

  7. Goddard, W., Hededtniemi, S.T., Jacobs, D.P., Srimani, P.K., Xu, Z.: Self-stabilizing graph protocols. Parallel Process. Lett. 18(1), 189–199 (2008)

    Article  MathSciNet  Google Scholar 

  8. Goddard, W., Hedetniemi, S.T., Jacobs, D.P., Srimani, P.K.: A self-stabilizing distributed algorithm for minimal total domination in an arbitrary system graph. In: Proceedings of the 17th International Parallel and Distributed Processing Symposium, April 2003

    Google Scholar 

  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). https://doi.org/10.1007/3-540-45438-1_8

    Chapter  Google Scholar 

  10. Hedetniemi, S.M., Hedetniemi, S., Jacobs, D.P., Srimani, P.K.: Self-stabilizing algorithms for minimal dominating sets and maximal independent sets. Comput. Math. Appl. 46(5–6), 805–811 (2003)

    Article  MathSciNet  Google Scholar 

  11. Ikeda, M., Kamei, S., Kakugawa, H.: A space-optimal self-stabilizing algorithm for the maximal independent set problem. In: Proceedings of the 3rd International Conference on Parallel and Distributed Computing, Applications and Technologies (2002)

    Google Scholar 

  12. Kakugawa, H., Masuzawa, T.: A self-stabilizing minimal dominating set algorithm with safe convergence. In: International Parallel and Distributed Processing Symposium, April 2006

    Google Scholar 

  13. Kshemkalyani, A.D., Singhal, M.: Distributed Computing: Principles, Algorithms, and Systems, p. 634. Cambridge University Press, Cambridge (2008)

    Book  Google Scholar 

  14. Shukla, S.K., Rosenkrantz, D.J., Ravi, S.S.: Observations on self-stabilizing graph algorithms for anonymous networks. In: Proceedings of the 2nd Workshop on Self-Stabilizing Systems (1995)

    Google Scholar 

  15. Turau, V.: Linear self-stabilizing algorithms for the independent and dominating set problems using an unfair distributed scheduler. Inf. Process. Lett. 103(3), 88–93 (2007)

    Article  MathSciNet  Google Scholar 

  16. Watts, D.J., Strogatz, S.H.: Collective dynamics of ‘small-world’ networks. Nature 393, 440–442 (1998)

    Article  Google Scholar 

  17. Xu, Z., Hedetniemi, S.T., Goddard, W., Srimani, P.K.: A synchronous self-stabilizing minimal domination protocol in an arbitrary network graph. In: Das, S.R., Das, S.K. (eds.) IWDC 2003. LNCS, vol. 2918, pp. 26–32. Springer, Heidelberg (2003). https://doi.org/10.1007/978-3-540-24604-6_3

    Chapter  Google Scholar 

  18. Yen, L.H., Chen, Z.L.: Game-theoretic approach to self-stabilizing distributed formation of minimal multi-dominating sets. IEEE Trans. Parallel Distrib. Syst. 25(12), 3201–3210 (2014)

    Article  Google Scholar 

  19. Yen, L.H., Huang, J.Y., Turau, V.: Designing self-stabilizing systems using game theory. ACM Trans. Auton. Adapt. Syst. 11(3), 18:1–18:27 (2016). Article no. 18

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, National Chiao Tung University, Hsinchu, Taiwan

    Li-Hsing Yen & Guang-Hong Sun

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  1. Li-Hsing Yen
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  2. Guang-Hong Sun
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Correspondence to Li-Hsing Yen .

Editor information

Editors and Affiliations

  1. Swinburne University of Technology, Hawthorn, VIC, Australia

    Yang Xiang

  2. National Institute of Informatics, Tokyo, Japan

    Jingtao Sun

  3. University of Calabria, Rende (CS), Italy

    Giancarlo Fortino

  4. ICAR-CNR, Rende (CS), Italy

    Antonio Guerrieri

  5. Chung-Ang University, Seoul, Korea (Republic of)

    Jason J. Jung

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Yen, LH., Sun, GH. (2018). Game-Theoretic Approach to Self-stabilizing Minimal Independent Dominating Sets. In: Xiang, Y., Sun, J., Fortino, G., Guerrieri, A., Jung, J. (eds) Internet and Distributed Computing Systems. IDCS 2018. Lecture Notes in Computer Science(), vol 11226. Springer, Cham. https://doi.org/10.1007/978-3-030-02738-4_15

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  • DOI: https://doi.org/10.1007/978-3-030-02738-4_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-02737-7

  • Online ISBN: 978-3-030-02738-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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