A 3/2-approximation Algorithm for the Student-Project Allocation Problem

Cooper, F. and Manlove, D. (2018) A 3/2-approximation Algorithm for the Student-Project Allocation Problem. In: 17th International Symposium on Experimental Algorithms (SEA 2018), L'Aquila, Italy, 27-29 Jun 2018, 8:1-8:13. ISBN 9783959770705 (doi: 10.4230/LIPIcs.SEA.2018.8)

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The Student-Project Allocation problem with lecturer preferences over Students (SPA-S) comprises three sets of agents, namely students, projects and lecturers, where students have preferences over projects and lecturers have preferences over students. In this scenario we seek a stable matching, that is, an assignment of students to projects such that there is no student and lecturer who have an incentive to deviate from their assignee/s. We study SPA-ST, the extension of SPA-S in which the preference lists of students and lecturers need not be strictly ordered, and may contain ties. In this scenario, stable matchings may be of different sizes, and it is known that MAX SPA-ST, the problem of finding a maximum stable matching in SPA-ST, is NP-hard. We present a linear-time 3/2-approximation algorithm for MAX SPA-ST and an Integer Programming (IP) model to solve MAX SPA-ST optimally. We compare the approximation algorithm with the IP model experimentally using randomly-generated data. We find that the performance of the approximation algorithm easily surpassed the 3/2 bound, constructing a stable matching within 92% of optimal in all cases, with the percentage being far higher for many instances.

Item Type:Conference Proceedings
Glasgow Author(s) Enlighten ID:Manlove, Professor David and Cooper, Frances
Authors: Cooper, F., and Manlove, D.
College/School:College of Science and Engineering > School of Computing Science
Copyright Holders:Copyright © 2018 Frances Cooper and David Manlove
First Published:First published in 17th International Symposium on Experimental Algorithms (SEA 2018): 8:1-8:13
Publisher Policy:Reproduced under a Creative Commons License
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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