Student-project allocation with preferences over projects

Manlove, D.F. and O'Malley, G. (2008) Student-project allocation with preferences over projects. Journal of Discrete Algorithms, 6(4), pp. 553-560. (doi: 10.1016/j.jda.2008.07.003)

Abstract

We study the problem of allocating students to projects, where both students and lecturers have preferences over projects, and both projects and lecturers have capacities. In this context we seek a stable matching of students to projects, which respects these preference and capacity constraints. Here, the stability definition generalises the corresponding notion in the context of the classical Hospitals/Residents problem. We show that stable matchings can have different sizes, which motivates max-spa-p, the problem of finding maximum cardinality stable matching. We prove that max-spa-p is NP-hard and not approximable within δ, for some δ>1, unless P=NP. On the other hand, we give an approximation algorithm with a performance guarantee of 2 for max-spa-p.

• Item Type: Articles
• Keywords: Matching problem, stable matching, NP-hardness, approximation hardness, approximation algorithm
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Manlove, Professor David and O'Malley, Mr Gregg
• Authors: Manlove, D.F., and O'Malley, G.
• Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
• College/School: College of Science and Engineering > School of Computing Science
• Journal Name: Journal of Discrete Algorithms
• Publisher: Elsevier
• ISSN: 1570-8667
• ISSN (Online): 1570-8675
• Published Online: 06 August 2008
• Copyright Holders: Copyright © 2008 Elsevier
• First Published: First published in Journal of Discrete Algorithms 6(4):553-560
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher.

Project Code	Award No	Project Name	Principal Investigator	Funder's Name	Funder Ref	Lead Dept
43636	1	MATCH-UP - matching under preferences - algorithms and complexity	Robert Irving	Engineering & Physical Sciences Research Council (EPSRC)	EP/E011993/1	COM - COMPUTING SCIENCE