Two algorithms for the student-project allocation problem

Abraham, D.J., Irving, R.W. and Manlove, D.F. (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)

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, Professor David and Irving, Dr Robert
• Authors: Abraham, D.J., Irving, R.W., and Manlove, D.F.
• 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.