An Efficient Silent Self-stabilizing 1-Maximal Matching Algorithm Under Distributed Daemon for Arbitrary Networks

  • Michiko InoueEmail author
  • Fukuhito Ooshita
  • Sébastien Tixeuil
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10616)


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.


Self-stabilization 1-Maximal matching algorithm Unfair distributed daemon Arbitrary networks 


  1. 1.
    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.00384MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Blair, J.R.S., Hedetniemi, S.M., Hedetniemi, S.T., Jacobs, D.P.: Self-stabilizing maximum matchings. Congr. Numer. 153, 151–160 (2001)MathSciNetzbMATHGoogle Scholar
  3. 3.
    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)Google Scholar
  4. 4.
    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)Google Scholar
  5. 5.
    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)Google Scholar
  6. 6.
    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)Google Scholar
  7. 7.
    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)Google Scholar
  8. 8.
    Dijkstra, E.W.: Self-stabilizing systems in spite of distributed control. Commun. ACM 17(11), 643–644 (1974)CrossRefGoogle Scholar
  9. 9.
    Dubois, S., Tixeuil, S.: A taxonomy of daemons in self-stabilization. CoRR abs/1110.0334 (2011).
  10. 10.
    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_13CrossRefGoogle Scholar
  11. 11.
    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)Google Scholar
  12. 12.
    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)CrossRefGoogle Scholar
  13. 13.
    Hedetniemi, S.T., Jacobs, D.P., Srimani, P.K.: Maximal matching stabilizes in time \(O(m)\). Inf. Process. Lett. 80(5), 221–223 (2001)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Hsu, S.C., Huang, S.T.: A self-stabilizing algorithm for maximal matching. Inf. Process. Lett. 43(2), 77–81 (1992)MathSciNetCrossRefGoogle Scholar
  15. 15.
    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_17CrossRefGoogle Scholar
  16. 16.
    Karaata, M.H., Saleh, K.A.: Distributed self-stabilizing algorithm for finding maximum matching. Comput. Syst. Sci. Eng. 15(3), 175–180 (2000)Google Scholar
  17. 17.
    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)CrossRefGoogle Scholar
  18. 18.
    Manne, F., Mjelde, M., Pilard, L., Tixeuil, S.: A new self-stabilizing maximal matching algorithm. Theoret. Comput. Sci. 410(14), 1336–1345 (2009)MathSciNetCrossRefGoogle Scholar
  19. 19.
    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)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Tel, G.: Introduction to Distributed Algorithms. Cambridge University Press, Cambridge (2000)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Michiko Inoue
    • 1
    Email author
  • Fukuhito Ooshita
    • 1
  • Sébastien Tixeuil
    • 2
  1. 1.Nara Institute of Science and TechnologyIkomaJapan
  2. 2.UPMC Sorbonne Universités, LIP6 - CNRS 7606, IUFParisFrance

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