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

Manlove, D. , Milne, D. and Olaosebikan, S. (2020) Student-project allocation with preferences over projects: algorithmic and experimental results. Discrete Applied Mathematics, (doi: 10.1016/j.dam.2020.08.015) (Early Online Publication)

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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:Early Online Publication
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):0166-218X
Published Online:29 August 2020
Copyright Holders:Copyright © 2020 The Authors
First Published:First published in Discrete Applied Mathematics 2020
Publisher Policy:Reproduced under a Creative Commons licence

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
300808IP-MATCH: Integer Programming for Large and Complex Matching ProblemsDavid ManloveEngineering and Physical Sciences Research Council (EPSRC)EP/P028306/1Computing Science