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

Kwanashie, A., Irving, R. W., Manlove, D. F. and Sng, C. T.S. (2015) Profile-Based Optimal Matchings in the Student-Project Allocation Problem. In: Combinatorial Algorithms: 25th International Workshop on Combinatorial Algorithms (IWOCA 2014), Duluth, MN, USA, 15-17 Oct 2014, pp. 213-225. ISBN 9783319193151 (doi: 10.1007/978-3-319-19315-1_19)

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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.

Item Type:Conference Proceedings
Additional Information:The final publication is available at Springer via
Glasgow Author(s) Enlighten ID:Manlove, Professor David and Kwanashie, Mr Augustine and Irving, Dr Robert
Authors: Kwanashie, A., Irving, R. W., Manlove, D. F., and Sng, C. T.S.
College/School:College of Science and Engineering > School of Computing Science
Copyright Holders:Copyright © 2015 Springer International Publishing Switzerland
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher
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Data DOI:10.5525/gla.researchdata.253

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
607071Efficient Algorithms for Mechanism Design Without Monetary Transfer.David ManloveEngineering & Physical Sciences Research Council (EPSRC)EP/K010042/1COM - COMPUTING SCIENCE