Abstract
A distributed system is self-stabilizing if, regardless of the initial state, the system is guaranteed to reach a legitimate (correct) state in finite time. In 2007, Turau proposed the first linear-time self-stabilizing algorithm for the minimal dominating set (MDS) problem under an unfair distributed daemon [6]; this algorithm stabilizes in at most 9n moves, where n is the number of nodes. In 2008, Goddard et al. [2] proposed a 5n-move algorithm. In this paper, we present a 4n-move algorithm. We also prove that if an MDS-silent algorithm is preferred, then distance-1 knowledge is insufficient, where a self-stabilizing MDS algorithm is MDS-silent if it will not make any move when the starting configuration of the system is already an MDS.
This research was partially supported by the National Science Council of the Republic of China under the grants grant NSC100-2115-M-009-004-MY2.
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References
Dijkstra, E.W.: Self-stabilizing systems in spite of distributed control. Communication of the ACM 17(11), 643–644 (1974)
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)
Guellati, N., Kheddouci, H.: A survey on self-stabilizing algorithms for independent, domination, coloring, and matching in graphs. Journal Parallel and Distributed Computing 70(4), 406–415 (2010)
Haynes, T.W., Hedetniemi, S.T., Slater, P.J.: Fundamentals of Domination in Graphs. Marcel Dekker (1998)
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)
Turau, V.: Linear self-stabilizing algorithms for the independent and dominating set problems using an unfair distributed scheduler. Information Processing Letters 103(3), 88–93 (2007)
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)
Turau, V.: Efficient transformation of distance-2 self-stabilizing algorithms. Journal of Parallel and Distributed Computing 72, 603–612 (2012)
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)
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Chiu, W.Y., Chen, C. (2013). Linear-Time Self-stabilizing Algorithms for Minimal Domination in Graphs. In: Lecroq, T., Mouchard, L. (eds) Combinatorial Algorithms. IWOCA 2013. Lecture Notes in Computer Science, vol 8288. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45278-9_11
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DOI: https://doi.org/10.1007/978-3-642-45278-9_11
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