Two algorithms for the student-project allocation problem

Abraham, D.J., Irving, R.W. and Manlove, D.M. (2007) Two algorithms for the student-project allocation problem. Journal of Discrete Algorithms, 5(1), pp. 73-90. (doi:10.1016/j.jda.2006.03.006)

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Publisher's URL: http://dx.doi.org/10.1016/j.jda.2006.03.006

Abstract

We study the Student-Project Allocation problem (SPA), a generalisation of the classical Hospitals / Residents problem (HR). An instance of SPA involves a set of students, projects and lecturers. Each project is offered by a unique lecturer, and both projects and lecturers have capacity constraints. Students have preferences over projects, whilst lecturers have preferences over students. We present two optimal linear-time algorithms for allocating students to projects, subject to the preference and capacity constraints. In particular, each algorithm finds a stable matching of students to projects. Here, the concept of stability generalises the stability definition in the HR context. The stable matching produced by the first algorithm is simultaneously best-possible for all students, whilst the one produced by the second algorithm is simultaneously best-possible for all lecturers. We also prove some structural results concerning the set of stable matchings in a given instance of SPA. The SPA problem model that we consider is very general and has applications to a range of different contexts besides student-project allocation.

Item Type:Articles
Keywords:Stable matching problem; Preference lists; Linear-time algorithm; Student-optimal; Lecturer-optimal.
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Manlove, Dr David and Irving, Dr Robert
Authors: Abraham, D.J., Irving, R.W., and Manlove, D.M.
Subjects:Q Science > QA Mathematics > QA75 Electronic computers. Computer science
College/School:College of Science and Engineering > School of Computing Science
Journal Name:Journal of Discrete Algorithms
Publisher:Elsevier
ISSN:1570-8667
Copyright Holders:Copyright © 2007 Elsevier
First Published:First published in Journal of Discrete Algorithms 5(1):73-90
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher.

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