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Profile-Based Optimal Matchings in the Student/Project Allocation Problem

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Combinatorial Algorithms (IWOCA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8986))

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  • International Workshop on Combinatorial Algorithms

Abstract

In the Student/Project Allocation problem (spa) we seek to assign students to individual or group projects offered by lecturers. Students provide a list of projects they find acceptable in order of preference. Each student can be assigned to at most one project and there are constraints on the maximum number of students that can be assigned to each project and lecturer. We seek matchings of students to projects that are optimal with respect to profile, which is a vector whose rth component indicates how many students have their rth-choice project. We present an efficient algorithm for finding agreedy maximum matching in the spa context – this is a maximum matching whose profile is lexicographically maximum. We then show how to adapt this algorithm to find a generous maximum matching – this is a matching whose reverse profile is lexicographically minimum. Our algorithms involve finding optimal flows in networks. We demonstrate how this approach can allow for additional constraints, such as lecturer lower quotas, to be handled flexibly.

D.F. Manlove—Supported by Engineering and Physical Sciences Research Council grant EP/K010042/1.

C.T.S. Sng—Work done while at the School of Computing Science, University of Glasgow.

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References

  1. Abraham, D.J.: Algorithmics of two-sided matching problems. Master’s thesis, University of Glasgow, Department of Computing Science (2003)

    Google Scholar 

  2. Abraham, D.J., Irving, R.W., Manlove, D.F.: Two algorithms for the Student-Project allocation problem. J. Discrete Algorithms 5(1), 79–91 (2007)

    Article  MathSciNet  Google Scholar 

  3. El-Atta, A.H.A., Moussa, M.I.: Student project allocation with preference lists over (student, project) pairs. In: Proceedings of ICCEE 09: The 2nd International Conference on Computer and Electrical Engineering, pp. 375–379 (2009)

    Google Scholar 

  4. Ford, L.R., Fulkerson, D.R.: Flows in Networks. Princeton University Press, Princeton (1962)

    MATH  Google Scholar 

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

    MATH  Google Scholar 

  6. Huang, C.-C., Kavitha, T., Mehlhorn, K., Michail, D.: Fair matchings and related problems. In: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013), vol. 24, pp. 339–350 (2013)

    Google Scholar 

  7. Hylland, A., Zeckhauser, R.: The efficient allocation of individuals to positions. J. Polit. Econ. 87(2), 293–314 (1979)

    Article  Google Scholar 

  8. Irving, R.W.: Greedy matchings. Technical Report TR-2003-136, University of Glasgow, Department of Computing Science (2003)

    Google Scholar 

  9. Irving, R.W.: Greedy and generous matchings via a variant of the Bellman-Ford algorithm (2006) (Unpublished manuscript)

    Google Scholar 

  10. Irving, R.W., Kavitha, T., Mehlhorn, K., Michail, D., Paluch, K.: Rank-maximal matchings. ACM Trans. Algorithms 2(4), 602–610 (2006)

    Article  MathSciNet  Google Scholar 

  11. Iwama, K., Miyazaki, S., Yanagisawa, H.: Improved approximation bounds for the student-project allocation problem with preferences over projects. J. Discrete Algorithms 13, 59–66 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  12. Kwanashie, A., Irving, R.W., Manlove, D.F., Sng, C.T.S.: Profile-based optimal matchings in the Student/Project Allocation problem. CoRR Technical Report 1403.0751 (2014). http://arxiv.org/abs/1403.0751

  13. Manlove, D.F.: Algorithmics of Matching Under Preferences. World Scientific, Singapore (2013)

    Book  MATH  Google Scholar 

  14. Manlove, D.F., O’Malley, G.: Student project allocation with preferences over projects. J. Discrete Algorithms 6, 553–560 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  15. Mehlhorn, K., Michail, D.: Network problems with non-polynomial weights and applications (2006) (Unpublished manuscript)

    Google Scholar 

  16. Orlin, J.B.: A faster strongly polynomial minimum cost flow algorithm. Oper. Res. 41(2), 338–350 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  17. Sng, C.T.S.: Efficient Algorithms for Bipartite Matching Problems with Preferences. Ph.D. thesis, University of Glasgow, Department of Computing Science (2008)

    Google Scholar 

  18. Zelvyte, M.: The Student-Project Allocation problem: a network flow model. Honours project dissertation, University of Glasgow, School of Mathematics and Statistics (2014)

    Google Scholar 

  19. Zhou, L.: On a conjecture by Gale about one-sided matching problems. J. Econ. Theor. 52(1), 123–135 (1990)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. School of Computing Science, University of Glasgow, Glasgow, UK

    Augustine Kwanashie, Robert W. Irving & David F. Manlove

  2. EBay Inc., Austin, TX, USA

    Colin T. S. Sng

Authors
  1. Augustine Kwanashie
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  2. Robert W. Irving
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  3. David F. Manlove
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  4. Colin T. S. Sng
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Correspondence to Augustine Kwanashie .

Editor information

Editors and Affiliations

  1. Faculty of Mathematics and Physics, Charles University, Praha, Czech Republic

    Kratochvíl Jan

  2. University of Newcastle, Newcastle, New South Wales, Australia

    Mirka Miller

  3. University of Minnesota, Duluth Department of Mathematics, Duluth, Minnesota, USA

    Dalibor Froncek

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Kwanashie, A., Irving, R.W., Manlove, D.F., Sng, C.T.S. (2015). Profile-Based Optimal Matchings in the Student/Project Allocation Problem. In: Jan, K., Miller, M., Froncek, D. (eds) Combinatorial Algorithms. IWOCA 2014. Lecture Notes in Computer Science(), vol 8986. Springer, Cham. https://doi.org/10.1007/978-3-319-19315-1_19

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  • DOI: https://doi.org/10.1007/978-3-319-19315-1_19

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  • Print ISBN: 978-3-319-19314-4

  • Online ISBN: 978-3-319-19315-1

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