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Approximating Stable Matchings with Ties of Bounded Size

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Algorithmic Game Theory (SAGT 2020)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 12283))

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Abstract

Finding a stable matching is one of the central problems in algorithmic game theory. If participants are allowed to have ties and incomplete lists, computing a stable matching of maximum cardinality is known to be NP-hard. In this paper we present a \((3L-2)/(2L-1)\)-approximation algorithm for the stable matching problem with ties of size at most L and incomplete preferences. Our result matches the known lower bound on the integrality gap for the associated LP formulation.

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References

  1. Bauckholt, F., Pashkovich, K., Sanità, L.: On the approximability of the stable marriage problem with one-sided ties. ArXiv e-prints (2018)

    Google Scholar 

  2. Chiang, R., Pashkovich, K.: On the approximability of the stable matching problem with ties of size two. Algorithmica 1–19 (2020). https://doi.org/10.1007/s00453-020-00703-9

  3. David, M.: Algorithmics of Matching Under Preferences, vol. 2. World Scientific, Singapore (2013)

    Google Scholar 

  4. Gale, D., Shapley, L.: College admissions and the stability of marriage. Am. Math. Monthly 69(1), 9–15 (1962)

    Article  MathSciNet  Google Scholar 

  5. Gale, D., Sotomayor, M.: Some remarks on the stable matching problem. Discrete Appl. Math. 11(3), 223–232 (1985)

    Article  MathSciNet  Google Scholar 

  6. Huang, C.-C., Kavitha, T.: Improved approximation algorithms for two variants of the stable marriage problem with ties. Math. Program. 353–380 (2015). https://doi.org/10.1007/s10107-015-0923-0

  7. Iwama, K., Miyazaki, S., Yamauchi, N.: A 1.875-approximation algorithm for the stable marriage problem. In: 18th Symposium on Discrete Algorithms (SODA), pp. 288–297 (2007)

    Google Scholar 

  8. Iwama, K., Miyazaki, S., Yanagisawa, H.: A 25/17-approximation algorithm for the stable marriage problem with one-sided ties. Algorithmica 68(3), 758–775 (2014). https://doi.org/10.1007/s00453-012-9699-2

    Article  MathSciNet  MATH  Google Scholar 

  9. Király, Z.: Better and simpler approximation algorithms for the stable marriage problem. Algorithmica 60(1), 3–20 (2011)

    Article  MathSciNet  Google Scholar 

  10. Király, Z.: Linear time local approximation algorithm for maximum stable marriage. Algorithms 6(3), 471–484 (2013)

    Article  MathSciNet  Google Scholar 

  11. Lam, C.K.: Algorithms for stable matching with indifferences. Ph.D. thesis, University of Texas at Austin (2019)

    Google Scholar 

  12. Lam, C.K., Plaxton, C.G.: A \((1+1/e)\)-approximation algorithm for maximum stable matching with one-sided ties and incomplete lists. In: Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 2823–2840. SIAM, Philadelphia (2019). https://doi.org/10.1137/1.9781611975482.175

  13. Lam, C.-K., Plaxton, C.G.: Maximum stable matching with one-sided ties of bounded length. In: Fotakis, D., Markakis, E. (eds.) SAGT 2019. LNCS, vol. 11801, pp. 343–356. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-30473-7_23

    Chapter  Google Scholar 

  14. Manlove, D.F., Irving, R.W., Iwama, K., Miyazaki, S., Morita, Y.: Hard variants of stable marriage. Theoret. Comput. Sci. 276(1–2), 261–279 (2002). https://doi.org/10.1016/S0304-3975(01)00206-7

    Article  MathSciNet  MATH  Google Scholar 

  15. McDermid, E.: A 3/2-approximation algorithm for general stable marriage. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds.) ICALP 2009, Part I. LNCS, vol. 5555, pp. 689–700. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-02927-1_57

    Chapter  Google Scholar 

  16. Paluch, K.: Faster and simpler approximation of stable matchings. Algorithms 7(2), 189–202 (2014)

    Article  MathSciNet  Google Scholar 

  17. Yanagisawa, H.: Approximation algorithms for stable marriage problems. Ph.D. thesis, Kyoto University (2007)

    Google Scholar 

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Authors and Affiliations

  1. University of Waterloo, Waterloo, ON, N2L 3G1, Canada

    Jochen Koenemann & Natig Tofigzade

  2. University of Ottawa, Ottawa, ON, K1N 6N5, Canada

    Kanstantsin Pashkovich

Authors
  1. Jochen Koenemann
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  2. Kanstantsin Pashkovich
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  3. Natig Tofigzade
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Correspondence to Natig Tofigzade .

Editor information

Editors and Affiliations

  1. Institute of Mathematics, Augsburg University, Augsburg, Germany

    Tobias Harks

  2. Institute of Mathematics, Technical University Berlin, Berlin, Germany

    Max Klimm

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Koenemann, J., Pashkovich, K., Tofigzade, N. (2020). Approximating Stable Matchings with Ties of Bounded Size. In: Harks, T., Klimm, M. (eds) Algorithmic Game Theory. SAGT 2020. Lecture Notes in Computer Science(), vol 12283. Springer, Cham. https://doi.org/10.1007/978-3-030-57980-7_12

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  • DOI: https://doi.org/10.1007/978-3-030-57980-7_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-57979-1

  • Online ISBN: 978-3-030-57980-7

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