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International Conference on Combinatorial Optimization and Applications

COCOA 2014: Combinatorial Optimization and Applications pp 429–443Cite as

Integer Programming Methods for Special College Admissions Problems

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8881))

Abstract

We develop Integer Programming (IP) solutions for some special college admission problems arising from the Hungarian higher education admission scheme. We focus on four special features, namely the solution concept of stable score-limits, the presence of lower and common quotas, and paired applications. We note that each of the latter three special feature makes the college admissions problem NP-hard to solve. Currently, a heuristic based on the Gale-Shapley algorithm is being used in the application. The IP methods that we propose are not only interesting theoretically, but may also serve as an alternative solution concept for this practical application, and other similar applications.

P. Biró: Visiting faculty at the Economics Department, Stanford University in year 2014. Supported by the Hungarian Academy of Sciences under its Momentum Programme (LD-004/2010) and also by OTKA grant no. K108673.

L. McBride: Supported by a SICSA Prize PhD Studentship.

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Notes

  1. 1.

    The 2012 Nobel-Prize in Economic Sciences has been awarded to Alvin Roth and Lloyd Shapley for the theory of stable allocations and the practice of market design.

  2. 2.

    In a famous study Roth [21] analysed the nature and the long term success of a dozen resident allocation schemes established in the UK in the late seventies. He found that two schemes produced stable outcomes and both of them remained in use. From the remaining six ones, that did not always produce stable matchings, four were eventually abandoned. The two programs that were not always produced stable solutions but yet remained used were based on linear programming techniques and has been operated for the two smallest market. Ünver [26] studied these programs and the possible reasons of their survival in detail.

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Authors and Affiliations

  1. Research Centre for Economic and Regional Studies, Institute of Economics, Hungarian Academy of Sciences, Budaörsi út 45, Budapest, 1112, Hungary

    Péter Biró

  2. School of Computing Science, University of Glasgow, Sir Alwyn Williams Building, Glasgow, G12 8QQ, UK

    Iain McBride

Authors
  1. Péter Biró
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  2. Iain McBride
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Correspondence to Péter Biró .

Editor information

Editors and Affiliations

  1. Zhejiang Normal University, Jinhua, Zhejiang, China

    Zhao Zhang

  2. University of Texas, Tyler, Texas, USA

    Lidong Wu

  3. University of Texas, Dallas, Texas, USA

    Wen Xu

  4. University of Texas, Dallas, USA

    Ding-Zhu Du

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Biró, P., McBride, I. (2014). Integer Programming Methods for Special College Admissions Problems. In: Zhang, Z., Wu, L., Xu, W., Du, DZ. (eds) Combinatorial Optimization and Applications. COCOA 2014. Lecture Notes in Computer Science(), vol 8881. Springer, Cham. https://doi.org/10.1007/978-3-319-12691-3_32

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  • DOI: https://doi.org/10.1007/978-3-319-12691-3_32

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-12690-6

  • Online ISBN: 978-3-319-12691-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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