Super-stability in the Student-Project Allocation Problem with Ties

Olaosebikan, S. and Manlove, D. (2018) Super-stability in the Student-Project Allocation Problem with Ties. In: 12th Annual International Conference on Combinatorial Optimization and Applications (COCOA 2018), Atlanta, GA, USA, 15-17 Dec 2018, pp. 357-371. ISBN 9783030046507 (doi:10.1007/978-3-030-04651-4_24)

Olaosebikan, S. and Manlove, D. (2018) Super-stability in the Student-Project Allocation Problem with Ties. In: 12th Annual International Conference on Combinatorial Optimization and Applications (COCOA 2018), Atlanta, GA, USA, 15-17 Dec 2018, pp. 357-371. ISBN 9783030046507 (doi:10.1007/978-3-030-04651-4_24)

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Abstract

The Student-Project Allocation problem with lecturer preferences over Students ( Open image in new window ) involves assigning students to projects based on student preferences over projects, lecturer preferences over students, and the maximum number of students that each project and lecturer can accommodate. This classical model assumes that preference lists are strictly ordered. Here, we study a generalisation of Open image in new window where ties are allowed in the preference lists of students and lecturers, which we refer to as the Student-Project Allocation problem with lecturer preferences over Students with Ties ( Open image in new window ). We investigate stable matchings under the most robust definition of stability in this context, namely super-stability. We describe the first polynomial-time algorithm to find a super-stable matching or to report that no such matching exists, given an instance of Open image in new window . Our algorithm runs in O(L) time, where L is the total length of all the preference lists. Finally, we present results obtained from an empirical evaluation of the linear-time algorithm based on randomly-generated Open image in new window instances. Our main finding is that, whilst super-stable matchings can be elusive, the probability of such a matching existing is significantly higher if ties are restricted to the lecturers’ preference lists.

Item Type:Conference Proceedings
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Manlove, Professor David and Olaosebikan, Sofiat Olamiji
Authors: Olaosebikan, S., and Manlove, D.
College/School:College of Science and Engineering > School of Computing Science
ISSN:0302-9743
ISBN:9783030046507
Published Online:16 November 2018
Copyright Holders:Copyright © 2018 Springer Nature Switzerland AG
First Published:First published in Lecture Notes in Computer Science 11346: 357-371
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