Abstract
The matching problem asks for a large set of disjoint edges in a graph. It is a problem that has received considerable attention in both the sequential and self-stabilizing literature. Previous work has resulted in self-stabilizing algorithms for computing a maximal (\(\frac{1}{2}\)-approximation) matching in a general graph, as well as computing a \(\frac{2}{3}\)-approximation on more specific graph types. In the following we present the first self-stabilizing algorithm for finding a \(\frac{2}{3}\)-approximation to the maximum matching problem in a general graph. We show that our new algorithm stabilizes in at most exponential time under a distributed adversarial daemon, and O(n 2) rounds under a distributed fair daemon, where n is the number of nodes in the graph.
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References
Blair, J.R.S., Manne, F.: Efficient self-stabilizing algorithms for tree networks. In: ICDCS 2003: Proceedings of the 23rd International Conference on Distributed Computing Systems, Washington, DC, USA, pp. 20–26. IEEE Computer Society Press, Los Alamitos (2003)
Danturi, P., Nesterenko, M., Tixeuil, S.: Self-stabilizing philosophers with generic conflicts. In: Datta, A.K., Gradinariu, M. (eds.) SSS 2006. LNCS, vol. 4280, pp. 214–230. Springer, Heidelberg (2006)
Dijkstra, E.W.: Self-stabilizing systems in spite of distributed control. Commun. ACM 17(11), 643–644 (1974)
Dolev, S.: Self-Stabilization. MIT Press, Cambridge (2000)
Ghosh, S., Gupta, A., Karaata, M.H., Pemmaraju, S.V.: Self-stabilizing dynamic programming algorithms on trees. In: Proceedings of the Second Workshop on Self-Stabilizing Systems (WSSS 1995), Las Vegas, pp. 11.1–11.15 (1995)
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: IPDPS 2003: Proceedings of the 17th International Symposium on Parallel and Distributed Processing, Washington, DC, USA, p. 162.2. IEEE Computer Society Press, Los Alamitos (2003)
Goddard, W., Hedetniemi, S.T., Jacobs, D.P., Trevisan, V.: Distance-k knowledge in self-stabilizing algorithms. Theor. Comput. Sci. 399(1-2), 118–127 (2008)
Goddard, W., Hedetniemi, S.T., Shi, Z.: An anonymous self-stabilizing algorithm for 1-maximal matching in trees. In: PDPTA 2006: Proceedings of the International Conference on Parallel and Distributed Processing Techniques and Applications & Conference on Real-Time Computing Systems and Applications, vol. 2, pp. 797–803. CSREA Press (2006)
Gradinariu, M., Johnen, C.: Self-stabilizing neighborhood unique naming under unfair scheduler. In: Sakellariou, R., Keane, J.A., Gurd, J.R., Freeman, L. (eds.) Euro-Par 2001, vol. 2150, pp. 458–465. Springer, Heidelberg (2001)
Gradinariu, M., Tixeuil, S.: Conflict managers for self-stabilization without fairness assumption. In: ICDCS 2007: Proceedings of the International Conference on Distributed Computing Systems. IEEE Computer Society Press, Los Alamitos (2007)
Hedetniemi, S.T., Jacobs, D.P., Srimani, P.K.: Maximal matching stabilizes in time O(m). Inf. Process. Lett. 80(5), 221–223 (2001)
Hopcroft, J.E., Karp, R.M.: An n5/2 algorithm for maximum matchings in bipartite graphs. SIAM J. Comput. 2(4), 225–231 (1973)
Hsu, S.-C., Huang, S.-T.: A self-stabilizing algorithm for maximal matching. Inf. Process. Lett. 43(2), 77–81 (1992)
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)
Tel, G.: Maximal matching stabilizes in quadratic time. Inf. Process. Lett. 49(6), 271–272 (1994)
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Manne, F., Mjelde, M., Pilard, L., Tixeuil, S. (2008). A Self-stabilizing \(\frac{2}{3}\)-Approximation Algorithm for the Maximum Matching Problem. In: Kulkarni, S., Schiper, A. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2008. Lecture Notes in Computer Science, vol 5340. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89335-6_10
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DOI: https://doi.org/10.1007/978-3-540-89335-6_10
Publisher Name: Springer, Berlin, Heidelberg
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