Abstract
We present a new self-stabilizing 1-maximal matching algorithm that works under the distributed unfair daemon for arbitrarily shaped networks. The 1-maximal matching is a \(\frac{2}{3}\)-approximation of a maximum matching, a significant improvement over the \(\frac{1}{2}\)-approximation that is guaranteed by a maximal matching. Our algorithm is efficient (its stabilization time is O(e) moves, where e denotes the number of edges in the network). Besides, our algorithm is optimal with respect to identifiers locality (we assume node identifiers are distinct up to distance three, a necessary condition to withstand arbitrary networks).
The proposed algorithm closes the complexity gap between two recent works: Inoue et al. presented a 1-maximal matching algorithm that is O(e) moves but requires the network topology not to contain a cycle of size of multiple of three; Cohen et al. consider arbitrary topology networks but requires \(O(n^3)\) moves to stabilize (where n denotes the number of nodes in the network). Our solution preserves the better complexity of O(e) moves, yet considers arbitrary networks, demonstrating that previous restrictions were unnecessary to preserve complexity results.
A preliminary brief announcement of this work appears in the proceedings of the 36th ACM Symposium on Principles of Distributed Computing (PODC 2017). This work was supported by JSPS KAKENHI Grant Number 26330084. Part of this work was carried out while the third author was visiting NAIST thanks to Erasmus Mundus TEAM program.
References
Asada, Y., Ooshita, F., Inoue, M.: An efficient silent self-stabilizing 1-maximal matching algorithm in anonymous networks. J. Graph Algorithms Appl. 20(1), 59–78 (2016). doi:10.7155/jgaa.00384
Blair, J.R.S., Hedetniemi, S.M., Hedetniemi, S.T., Jacobs, D.P.: Self-stabilizing maximum matchings. Congr. Numer. 153, 151–160 (2001)
Blair, J.R.S., Manne, F.: Efficient self-stabilizing algorithms for tree networks. In: Proceedings of 23rd International Conference on Distributed Computing Systems, pp. 20–26. IEEE (2003)
Chattopadhyay, S., Higham, L., Seyffarth, K.: Dynamic and self-stabilizing distributed matching. In: Proceedings of the Twenty-First Annual Symposium on Principles of Distributed Computing, pp. 290–297. ACM (2002)
Cohen, J., Maâmra, K., Manoussakis, G., Pilard, L.: Polynomial self-stabilizing maximal matching algorithm with approximation ratio 2/3. In: International Conference on Principles of Distributed Systems (2016)
Datta, A.K., Larmoreand, L.L., Masuzawa, T.: Maximum matching for anonymous trees with constant space per process. In: Proceedings of International Conference on Principles of Distributed Systems, pp. 1–16 (2015)
Devismes, S., Masuzawa, T., Tixeuil, S.: Communication efficiency in self-stabilizing silent protocols. In: Proceedings of 23rd International Conference on Distributed Computing Systems, pp. 474–481. IEEE (2009)
Dijkstra, E.W.: Self-stabilizing systems in spite of distributed control. Commun. ACM 17(11), 643–644 (1974)
Dubois, S., Tixeuil, S.: A taxonomy of daemons in self-stabilization. CoRR abs/1110.0334 (2011). http://arxiv.org/abs/1110.0334
Dubois, S., Tixeuil, S., Zhu, N.: The byzantine brides problem. In: Kranakis, E., Krizanc, D., Luccio, F. (eds.) FUN 2012. LNCS, vol. 7288, pp. 107–118. Springer, Heidelberg (2012). doi:10.1007/978-3-642-30347-0_13
Goddard, W., Hedetniemi, S.T., Shi, Z., et al.: An anonymous self-stabilizing algorithm for 1-maximal matching in trees. In: Proceedings of International Conference on Parallel and Distributed Processing Techniques and Applications, pp. 797–803 (2006)
Guellati, N., Kheddouci, H.: A survey on self-stabilizing algorithms for independence, domination, coloring, and matching in graphs. J. Parallel Distrib. Comput. 70(4), 406–415 (2010)
Hedetniemi, S.T., Jacobs, D.P., Srimani, P.K.: Maximal matching stabilizes in time \(O(m)\). Inf. Process. Lett. 80(5), 221–223 (2001)
Hsu, S.C., Huang, S.T.: A self-stabilizing algorithm for maximal matching. Inf. Process. Lett. 43(2), 77–81 (1992)
Inoue, M., Ooshita, F., Tixeuil, S.: An efficient silent self-stabilizing 1-maximal matching algorithm under distributed daemon without global identifiers. In: Bonakdarpour, B., Petit, F. (eds.) SSS 2016. LNCS, vol. 10083, pp. 195–212. Springer, Cham (2016). doi:10.1007/978-3-319-49259-9_17
Karaata, M.H., Saleh, K.A.: Distributed self-stabilizing algorithm for finding maximum matching. Comput. Syst. Sci. Eng. 15(3), 175–180 (2000)
Kimoto, M., Tsuchiya, T., Kikuno, T.: The time complexity of Hsu and Huang’s self-stabilizing maximal matching algorithm. IEICE Trans. Inf. Syst. E93–D(10), 2850–2853 (2010)
Manne, F., Mjelde, M., Pilard, L., Tixeuil, S.: A new self-stabilizing maximal matching algorithm. Theoret. Comput. Sci. 410(14), 1336–1345 (2009)
Manne, F., Mjelde, M., Pilard, L., Tixeuil, S.: A self-stabilizing 2/3-approximation algorithm for the maximum matching problem. Theoret. Comput. Sci. 412(40), 5515–5526 (2011)
Tel, G.: Introduction to Distributed Algorithms. Cambridge University Press, Cambridge (2000)
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Inoue, M., Ooshita, F., Tixeuil, S. (2017). An Efficient Silent Self-stabilizing 1-Maximal Matching Algorithm Under Distributed Daemon for Arbitrary Networks. In: Spirakis, P., Tsigas, P. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2017. Lecture Notes in Computer Science(), vol 10616. Springer, Cham. https://doi.org/10.1007/978-3-319-69084-1_7
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