Two algorithms for the Student-Project Allocation problem

Authors:
David J. Abraham;Robert W. Irving;David F. Manlove
Affiliations:
Computer Science Department, Carnegie-Mellon University, 5000 Forbes Ave, Pittsburgh PA 15213-3890, USA;Department of Computing Science, University of Glasgow, Glasgow G12 8QQ, UK;Department of Computing Science, University of Glasgow, Glasgow G12 8QQ, UK
Venue:
Journal of Discrete Algorithms
Year:
2007

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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.