Student-project allocation with preferences over projects: algorithmic and experimental results

Manlove, D. , Milne, D. and Olaosebikan, S. (2022) Student-project allocation with preferences over projects: algorithmic and experimental results. Discrete Applied Mathematics, 308, pp. 220-234. (doi: 10.1016/j.dam.2020.08.015)

Abstract

We study the Student-Project Allocation problem with lecturer preferences over Projects (spa-p). In this context it is known that stable matchings can have different sizes and the problem of finding a maximum size stable matching is NP-hard. There are two known approximation algorithms for max-spa-p, with performance guarantees 2 and . We show that max-spa-p is polynomial-time solvable if there is only one lecturer involved, and NP-hard to approximate within some constant if there are two lecturers involved. We also show that this problem remains NP-hard if each preference list is of length at most 3, with an arbitrary number of lecturers. We then describe an Integer Programming (IP) model to enable max-spa-p to be solved optimally in the general case. Following this, we present results arising from an empirical evaluation that investigates how the solutions produced by the approximation algorithms compare to optimal solutions obtained from the IP model, with respect to the size of the stable matchings constructed, on instances that are both randomly-generated and derived from real datasets.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Manlove, Professor David and Olaosebikan, Dr Sofiat and Milne, Mr Duncan
• Authors: Manlove, D., Milne, D., and Olaosebikan, S.
• College/School: College of Science and Engineering > School of Computing Science
• Journal Name: Discrete Applied Mathematics
• Publisher: Elsevier
• ISSN: 0166-218X
• ISSN (Online): 1872-6771
• Published Online: 29 August 2020
• Copyright Holders: Copyright © 2020 The Authors
• First Published: First published in Discrete Applied Mathematics 308: 220-234
• Publisher Policy: Reproduced under a Creative Commons licence

Project Code	Award No	Project Name	Principal Investigator	Funder's Name	Funder Ref	Lead Dept
300808		IP-MATCH: Integer Programming for Large and Complex Matching Problems	David Manlove	Engineering and Physical Sciences Research Council (EPSRC)	EP/P028306/1	Computing Science