The College Admissions problem with lower and common quotas

Biro, P., Fleiner, T., Irving, R.W. and Manlove, D.F. (2010) The College Admissions problem with lower and common quotas. Theoretical Computer Science, 411(34-36), pp. 3136-3153. (doi: 10.1016/j.tcs.2010.05.005)

Abstract

We study two generalised stable matching problems motivated by the current matching scheme used in the higher education sector in Hungary. The first problem is an extension of the College Admissions problem in which the colleges have lower quotas as well as the normal upper quotas. Here, we show that a stable matching may not exist and we prove that the problem of determining whether one does is NP-complete in general. The second problem is a different extension in which, as usual, individual colleges have upper quotas, but, in addition, certain bounded subsets of colleges have common quotas smaller than the sum of their individual quotas. Again, we show that a stable matching may not exist and the related decision problem is NP-complete. On the other hand, we prove that, when the bounded sets form a nested set system, a stable matching can be found by generalising, in non-trivial ways, both the applicant-oriented and college-oriented versions of the classical Gale–Shapley algorithm. Finally, we present an alternative view of this nested case using the concept of choice functions, and with the aid of a matroid model we establish some interesting structural results for this case.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Biro, Dr Peter and Irving, Dr Robert and Manlove, Professor David
• Authors: Biro, P., Fleiner, T., Irving, R.W., and Manlove, D.F.
• College/School: College of Science and Engineering > School of Computing Science
• Journal Name: Theoretical Computer Science
• Publisher: Elsevier
• ISSN: 0304-3975
• ISSN (Online): 1879-2294
• Published Online: 20 May 2010
• First Published: First published in Theoretical Computer Science 411(34-36):3136-3153
• 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	Computing Science