An Integer Programming Approach to the Student-Project Allocation Problem with Preferences over Projects

Manlove, D. , Milne, D. and Olaosebikan, S. (2018) An Integer Programming Approach to the Student-Project Allocation Problem with Preferences over Projects. In: International Symposium on Combinatorial Optimization (ISCO 2018), Marrakesh, Morocco, 11-13 Apr 2018, pp. 313-325. ISBN 9783319961507 (doi:10.1007/978-3-319-96151-4_27)

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Abstract

The Student-Project Allocation problem with preferences over Projects (SPA-P) involves sets of students, projects and lecturers, where the students and lecturers each have preferences over the projects. In this context, we typically seek a stable matching of students to projects (and lecturers). However, these stable matchings can have different sizes, and the problem of finding a maximum stable matching (MAX-SPA-P) is NP-hard. There are two known approximation algorithms for MAX-SPA-P, with performance guarantees of 2 and 32 . In this paper, we describe an Integer Programming (IP) model to enable MAX-SPA-P to be solved optimally. Following this, we present results arising from an empirical analysis that investigates how the solution produced by the approximation algorithms compares to the optimal solution 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. Our main finding is that the 32 -approximation algorithm finds stable matchings that are very close to having maximum cardinality.

Item Type:Conference Proceedings
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Manlove, Professor David and Olaosebikan, Ms Sofiat and Milne, Mr Duncan
Authors: Manlove, D., Milne, D., and Olaosebikan, S.
College/School:College of Science and Engineering > School of Computing Science
ISSN:0302-9743
ISBN:9783319961507
Published Online:18 July 2018
Copyright Holders:Copyright © 2018 Springer International Publishing AG, part of Springer Nature
First Published:First published in Combinatorial Optimization: 5th International Symposium, ISCO 2018, Marrakesh, Morocco, April 11–13, 2018, Revised Selected Papers: 313-325
Publisher Policy:Reproduced in accordance with the publisher copyright policy
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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
3008080IP-MATCH: Integer Programming for Large and Complex Matching ProblemsDavid ManloveEngineering and Physical Sciences Research Council (EPSRC)EP/P028306/1Computing Science