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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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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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Corresponding author

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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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19314-4

  • Online ISBN: 978-3-319-19315-1

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