Abstract
In [Dij74] Dijkstra introduced the notion of self-stabilizing algorithms and presented an algorithm with three states for the problem of mutual exclusion on a ring of processors. In [BD95] a similar three state algorithm with an upper bound of \(5\frac{3}{4}n^2+O(n)\) and a lower bound of \(\frac{1}{8}n^2-O(n)\) were presented for its stabilization time. For this later algorithm we prove an upper bound of \(1\frac{1}{2}n^2 + O(n)\), and show a lower bound of n 2 − O(n).
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References
Beauquier, J., Debas, O.: An optimal self-stabilizing algorithm for mutual exclusion on bidirectional non uniform rings. In: Proceedings of the Second Workshop on Self-Stabilizing Systems, pp. 17.1–17.13 (1995)
Burns, J.E., Gouda, M.G., Miller, R.E.: On relaxing interleaving assumptions. In: Proceedings of the MCC Workshop on Self-Stabilizing Systems, MCC Technical Report No. STP-379-89 (1989)
Beauquier, J., Johnen, C., Messika, S.: Brief announcement: Computing automatically the stabilization time against the worst and the best schedules. In: Dolev, S. (ed.) DISC 2006. LNCS, vol. 4167, pp. 543–547. Springer, Heidelberg (2006)
Cobb, J.A., Gouda, M.G.: Stabilization of general loop-free routing. Journal of Parallel and Distributed Computing 62(5), 922–944 (2002)
Chernoy, V., Shalom, M., Zaks, S.: On the performance of Dijkstra’s third self-stabilizing algorithm for mutual exclusion. In: 9th International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS), Paris, November 2007, pp. 114–123 (2007)
Chernoy, V., Shalom, M., Zaks, S.: A self-stabilizing algorithm with tight bounds for mutual exclusion on a ring (submitted for publication) (2008)
Dijkstra, E.W.: Self stabilizing systems in spite of distributed control. Communications of the Association of the Computing Machinery 17(11), 643–644 (1974)
Dijkstra, E.W.: A belated proof of self-stabilization. Distributed Computing 1, 5–6 (1986)
Dolev, S.: Self-Stabilization. MIT Press, Cambridge (2000)
Kessels, J.L.W.: An exercise in proving self-stabilization with a variant function. Information Processing Letters 29, 39–42 (1988)
Nakaminami, Y., Kakugawa, H., Masuzawa, T.: An advanced performance analysis of self-stabilizing protocols: stabilization time with transient faults during convergence. In: 20th International Parallel and Distributed Processing Symposium (IPDPS 2006), Rhodes Island, Greece, April 25-29 (2006)
Tsuchiya, T., Tokuda, Y., Kikuno, T.: Computing the stabilization times of self-stabilizing systems. IEICE Transactions on Fundamentals of Electronic Communications and Computer Sciences E83A(11), 2245–2252 (2000)
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Chernoy, V., Shalom, M., Zaks, S. (2008). On the Performance of Beauquier and Debas’ Self-stabilizing Algorithm for Mutual Exclusion. 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_19
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DOI: https://doi.org/10.1007/978-3-540-69355-0_19
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