Abstract
Stable marriage is a problem of matching in a bipartite graph, introduced in an economic context by Gale and Shapley. In this problem, each node has preferences for matching with its neighbors. The final matching should satisfy these preferences such that in no unmatched pair both nodes prefer to be matched together. The problem has a lot of useful applications (two sided markets, migration of virtual machines in Cloud computing, content delivery on the Internet, etc.). There even exist companies dedicated solely to administering stable matching programs. Numerous algorithms have been designed for solving this problem (and its variants), in different contexts, including distributed ones. However, to the best of our knowledge, none of the distributed solutions is self-stabilizing (self-stabilization is a formal framework that allows dealing with transient corruptions of memory and channels). We present a self-stabilizing stable matching solution, in the model of composite atomicity (state-reading model), under an unfair distributed scheduler. The algorithm is given with a formal proof of correctness and an upper bound on its time complexity in terms of moves and steps.
This is a preview of subscription content, log in via an institution to check access.
References
Ackermann, H., Goldberg, P.W., Mirrokni, V.S., Röglin, H., Vöcking, B.: Uncoordinated two-sided matching markets. SIAM J. Comput. 40(1), 92–106 (2011)
Amira, N., Giladi, R., Lotker, Z.: Distributed weighted stable marriage problem. In: Patt-Shamir, B., Ekim, T. (eds.) SIROCCO 2010. LNCS, vol. 6058, pp. 29–40. Springer, Heidelberg (2010). doi:10.1007/978-3-642-13284-1_4
Awerbuch, B., Kutten, S., Mansour, Y., Patt-Shamir, B., Varghese, G.: A time-optimal self-stabilizing synchronizer using a phase clock. IEEE Trans. Dependable Secur. Comput. 4(3), 180–190 (2007)
Boulinier, C., Petit, F., Villain, V.: When graph theory helps self-stabilization. In: PODC, pp. 150–159 (2004)
Brito, I., Meseguer, P.: Distributed stable marriage problem. In: 6th Workshop on Distributed Constraint Reasoning at IJCAI, vol. 5, pp. 135–147 (2005)
Chuang, S., Goel, A., McKeown, N., Prabhakar, B.: Matching output queueing with a combined input/output-queued switch. IEEE J. Sel. Areas Commun. 17(6), 1030–1039 (1999)
Dijkstra, E.W.: Self-stabilizing systems in spite of distributed control. Commun. ACM 17(11), 643–644 (1974)
Floren, P., Kaski, P., Polishchuk, V., Suomela, J.: Almost stable matchings by truncating the Gale-Shapley algorithm. Algorithmica 58(1), 102–118 (2010)
Gale, D., Shapley, L.S.: College admissions and the stability of marriage. Am. Math. Mon. 120(5), 386–391 (1962)
Ghosh, S.: Distributed Systems: An Algorithmic Approach, 2nd edn. Chapman & Hall/CRC, Boca Raton (2014)
Golle, P.: A private stable matching algorithm. In: Crescenzo, G., Rubin, A. (eds.) FC 2006. LNCS, vol. 4107, pp. 65–80. Springer, Heidelberg (2006). doi:10.1007/11889663_5
Gonczarowski, Y.A., Nisan, N., Ostrovsky, R., Rosenbaum, W.: A stable marriage requires communication. In: SODA 2015, pp. 1003–1017 (2015)
Gusfield, D., Irving, R.W.: The Stable Marriage Problem - Structure and Algorithms. Foundations of Computing Series. MIT Press, Cambridge (1989)
Kim, G., Lee, W.: Stable matching with ties for cloud-assisted smart tv services. In: ICCE, pp. 558–559 (2014)
Kipnis, A., Patt-Shamir, B.: A note on distributed stable matching. In: ICDCS, pp. 466–473 (2009)
Knuth, D.E.: Mariages stables et leurs relations avec d’autres problemes combinatoires. Les Presses de l’Universite de Montreal (1976)
Laveau, M., Manoussakis, G., Beauquier, J., Bernard, T., Burman, J., Cohen, J., Pilard, L.: Self-stabilizing distributed stable marriage. Research report (2017)
Maggs, B.M., Sitaraman, R.K.: Algorithmic nuggets in content delivery. Comput. Commun. Rev. 45(3), 52–66 (2015)
Manlove, D.F.: Algorithmics of Matching Under Preferences, vol. 2. World Scientific, Singapore (2013)
Ng, C., Hirschberg, D.S.: Lower bounds for the stable marriage problem and its variants. SIAM J. Comput. 19(1), 71–77 (1990)
Ostrovsky, R., Rosenbaum, W.: Fast distributed almost stable matchings. In: PODC 2015, pp. 101–108. ACM, New York (2015)
Khanchandani, P., Wattenhofer, R.: Distributed stable matching with similar preference lists. In: OPODIS. pp. 12:1–12:16 (2016)
Roth, A., Vande Vate, J.H.: Random paths to stability in two-sided matching. Econometrica 58(6), 1475–80 (1990)
Roth, A.E., Sotomayor, M.A.O.: Two-Sided Matching: A Study in Game-theoretic Modeling and Analysis. Cambridge University Press, Cambridge (1990)
Xu, H., Li, B.: Seen as stable marriages. In: INFOCOM, pp. 586–590 (2011)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Laveau, M. et al. (2017). Self-stabilizing Distributed Stable Marriage. 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_4
Download citation
DOI: https://doi.org/10.1007/978-3-319-69084-1_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-69083-4
Online ISBN: 978-3-319-69084-1
eBook Packages: Computer ScienceComputer Science (R0)