Skip to main content
SpringerLink
Log in
SpringerLink
Log in

Rotation-Based Formulation for Stable Matching

  • Conference paper
  • First Online:
Principles and Practice of Constraint Programming (CP 2017)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 10416))

Abstract

We introduce new CP models for the many-to-many stable matching problem. We use the notion of rotation to give a novel encoding that is linear in the input size of the problem. We give extra filtering rules to maintain arc consistency in quadratic time. Our experimental study on hard instances of sex-equal and balanced stable matching shows the efficiency of one of our propositions as compared with the state-of-the-art constraint programming approach.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Baïou, M., Balinski, M.: Many-to-many matching: stable polyandrous polygamy (or polygamous polyandry). Discrete Appl. Math. 101(1–3), 1–12 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bansal, V., Agrawal, A., Malhotra, V.S.: Polynomial time algorithm for an optimal stable assignment with multiple partners. Theor. Comput. Sci. 379(3), 317–328 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  3. Eirinakis, P., Magos, D., Mourtos, I., Miliotis, P.: Finding all stable pairs and solutions to the many-to-many stable matching problem. INFORMS J. Comput. 24(2), 245–259 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  4. Feder, T.: A new fixed point approach for stable networks and stable marriages. J. Comput. Syst. Sci. 45(2), 233–284 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  5. Fleiner, T., Irving, R.W., Manlove, D.: Efficient algorithms for generalized stable marriage and roommates problems. Theor. Comput. Sci. 381(1–3), 162–176 (2007)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  7. Gent, I.P., Irving, R.W., Manlove, D.F., Prosser, P., Smith, B.M.: A constraint programming approach to the stable marriage problem. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 225–239. Springer, Heidelberg (2001). doi:10.1007/3-540-45578-7_16

    Chapter  Google Scholar 

  8. Gusfield, D., Irving, R.W.: The Stable Marriage Problem - Structure and Algorithms. Foundations of Computing Series. MIT Press, Cambridge (1989)

    MATH  Google Scholar 

  9. Gusfield, D., Irving, R.W.: The Stable Marriage Problem: Structure and Algorithms. MIT Press, Cambridge (1989)

    MATH  Google Scholar 

  10. Hebrard, E.: Mistral, a constraint satisfaction library. In: Proceedings of the CP 2008 Third International CSP Solvers Competition, pp. 31–40 (2008)

    Google Scholar 

  11. Hebrard, E., Siala, M.: Explanation-based weighted degree. In: Salvagnin, D., Lombardi, M. (eds.) CPAIOR 2017. LNCS, vol. 10335, pp. 167–175. Springer, Cham (2017). doi:10.1007/978-3-319-59776-8_13

    Chapter  Google Scholar 

  12. Irving, R.W., Leather, P.: The complexity of counting stable marriages. SIAM J. Comput. 15(3), 655–667 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  13. Manlove, D.F., O’Malley, G., Prosser, P., Unsworth, C.: A constraint programming approach to the hospitals/residents problem. In: Hentenryck, P., Wolsey, L. (eds.) CPAIOR 2007. LNCS, vol. 4510, pp. 155–170. Springer, Heidelberg (2007). doi:10.1007/978-3-540-72397-4_12

    Chapter  Google Scholar 

  14. Manlove, D.F.: Algorithmics of Matching Under Preferences. Series on Theoretical Computer Science, vol. 2. WorldScientific, Singapore (2013)

    MATH  Google Scholar 

  15. Michel, L., Hentenryck, P.: Activity-based search for black-box constraint programming solvers. In: Beldiceanu, N., Jussien, N., Pinson, É. (eds.) CPAIOR 2012. LNCS, vol. 7298, pp. 228–243. Springer, Heidelberg (2012). doi:10.1007/978-3-642-29828-8_15

    Chapter  Google Scholar 

  16. Moskewicz, M.W., Madigan, C.F., Zhao, Y., Zhang, L., Malik, S.: Chaff: engineering an efficient SAT solver. In: Proceedings of the 38th Design Automation Conference, DAC 2001, Las Vegas, NV, USA, 18–22 June 2001, pp. 530–535 (2001)

    Google Scholar 

  17. Prosser, P.: Stable roommates and constraint programming. In: Simonis, H. (ed.) CPAIOR 2014. LNCS, vol. 8451, pp. 15–28. Springer, Cham (2014). doi:10.1007/978-3-319-07046-9_2

    Chapter  Google Scholar 

  18. Refalo, P.: Impact-based search strategies for constraint programming. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 557–571. Springer, Heidelberg (2004). doi:10.1007/978-3-540-30201-8_41

    Chapter  Google Scholar 

  19. Rossi, F., van Beek, P., Walsh, T. (eds.): Handbook of Constraint Programming. Foundations of Artificial Intelligence, vol. 2. Elsevier (2006)

    Google Scholar 

  20. Siala, M., O’Sullivan, B.: Revisiting two-sided stability constraints. In: Quimper, C.-G. (ed.) CPAIOR 2016. LNCS, vol. 9676, pp. 342–357. Springer, Cham (2016). doi:10.1007/978-3-319-33954-2_25

    Google Scholar 

  21. Unsworth, C., Prosser, P.: A specialised binary constraint for the stable marriage problem. In: Zucker, J.-D., Saitta, L. (eds.) SARA 2005. LNCS (LNAI), vol. 3607, pp. 218–233. Springer, Heidelberg (2005). doi:10.1007/11527862_16

    Chapter  Google Scholar 

  22. Unsworth, C., Prosser, P.: An n-ary constraint for the stable marriage problem. CoRR, abs/1308.0183 (2013)

    Google Scholar 

Download references

Acknowledgments

We thank the anonymous reviewers for their constructive comments that helped to improve the presentation of the paper.

We thank Begum Genc for generating the instances.

This publication has emanated from research conducted with the financial support of Science Foundation Ireland (SFI) under Grant Number SFI/12/RC/2289.

Author information

Authors and Affiliations

  1. Insight Centre for Data Analytics, Department of Computer Science, University College Cork, Cork, Ireland

    Mohamed Siala & Barry O’Sullivan

Authors
  1. Mohamed Siala
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Barry O’Sullivan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohamed Siala .

Editor information

Editors and Affiliations

  1. University of Toronto, Toronto, Ontario, Canada

    J. Christopher Beck

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Siala, M., O’Sullivan, B. (2017). Rotation-Based Formulation for Stable Matching. In: Beck, J. (eds) Principles and Practice of Constraint Programming. CP 2017. Lecture Notes in Computer Science(), vol 10416. Springer, Cham. https://doi.org/10.1007/978-3-319-66158-2_17

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-66158-2_17

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-66157-5

  • Online ISBN: 978-3-319-66158-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation