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)

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Publisher's URL: http://dx.doi.org/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:Manlove, Dr David and Biro, Dr Peter and Irving, Dr Robert
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

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
436361MATCH-UP - matching under preferences - algorithms and complexityRobert IrvingEngineering & Physical Sciences Research Council (EPSRC)EP/E011993/1Computing Science