Document Open Access Logo

Stable Matching with Evolving Preferences

Authors Varun Kanade, Nikos Leonardos, Frédéric Magniez

Thumbnail PDF


  • Filesize: 0.49 MB
  • 13 pages

Document Identifiers

Author Details

Varun Kanade
Nikos Leonardos
Frédéric Magniez

Cite AsGet BibTex

Varun Kanade, Nikos Leonardos, and Frédéric Magniez. Stable Matching with Evolving Preferences. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 60, pp. 36:1-36:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2016)


We consider the problem of stable matching with dynamic preference lists. At each time-step, the preference list of some player may change by swapping random adjacent members. The goal of a central agency (algorithm) is to maintain an approximately stable matching, in terms of number of blocking pairs, at all time-steps. The changes in the preference lists are not reported to the algorithm, but must instead be probed explicitly. We design an algorithm that in expectation and with high probability maintains a matching that has at most O((log n)^2 blocking pairs.
  • Stable Matching
  • Dynamic Data


  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    PDF Downloads


  1. A. Anagnostopoulos, R. Kumar, M. Mahdian, and E. Upfal. Sorting and selection on dynamic data. Theoretical Computer Science, 412(24):2564-2576, 2011. Selected Papers from 36th International Colloquium on Automata, Languages and Programming. URL:
  2. A. Anagnostopoulos, R. Kumar, M. Mahdian, E. Upfal, and F. Vandin. Algorithms on evolving graphs. In Proc. of 3rd Innovations in Theoretical Computer Science, 2012. Google Scholar
  3. D. Eppstein, Z. Galil, and G. F. Italiano. Dynamic graph algorithms. In M. Atallah, editor, Algorithms and Theory of Computation Handbook, chapter 8. CRC Press, 1999. Google Scholar
  4. D. Gale and L. S. Shapley. College admissions and the stability of marriage. The American Mathematical Monthly, 69(1):9-15, 1962. Google Scholar
  5. M. Gupta and R. Peng. Fully dynamic (1+ e)-approximate matchings. In Proc. of 54th IEEE Foundations of Computer Science, pages 548-557, Oct 2013. URL:
  6. D. Knuth. Stable Marriage and Its Relation to Other Combinatorial Problems: An Introduction to the Mathematical Analysis of Algorithms. CRM proceedings &lecture notes. American Mathematical Society, 1997. Google Scholar
  7. David Asher Levin, Yuval Peres, and Elizabeth Lee Wilmer. Markov Chains and Mixing Times. American Mathematical Society, 2009. Google Scholar
  8. C. McDiarmid. Concentration. In M. Habib, C. McDiarmid, J. Ramirez-Alfonsin, and B. Reed, editors, Probabilistic Methods for Algorithmic Discrete Mathematics, volume 16 of Algorithms and Combinatorics, pages 195-248. Springer Berlin Heidelberg, 1998. URL:
  9. R. Motwani and P. Raghavan. Randomized Algorithms. Cambridge International Series on Parallel Computation. Cambridge University Press, 1995. Google Scholar
  10. O. Neiman and S. Solomon. Simple deterministic algorithms for fully dynamic maximal matching. In Proc. of 45th ACM Symposium on Theory of Computing, pages 745-754, 2013. URL:
  11. K. Onak and R. Rubinfeld. Maintaining a large matching and a small vertex cover. In Proc. of 42nd ACM Symposium on Theory of Computing, pages 457-464, 2010. URL:
  12. L. B. Wilson. An analysis of the stable marriage assignment algorithm. BIT Numerical Mathematics, 12(4):569-575, 1972. Google Scholar
Questions / Remarks / Feedback

Feedback for Dagstuhl Publishing

Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail