Approximability results for stable marriage problems with ties

Halldorsson, M., Irving, R.W., Iwama, K., Manlove, D. F., Miyazaki, S., Morita, Y. and Scott, S. (2003) Approximability results for stable marriage problems with ties. Theoretical Computer Science, 306(1-3), pp. 431-447. (doi: 10.1016/S0304-3975(03)00321-9)

Abstract

We consider instances of the classical stable marriage problem in which persons may include ties in their preference lists. We show that, in such a setting, strong lower bounds hold for the approximability of each of the problems of finding an egalitarian, minimum regret and sex-equal stable matching. We also consider stable marriage instances in which persons may express unacceptable partners in addition to ties. In this setting, we prove that there are constants delta, delta' such that each of the problems of approximating a maximum and minimum cardinality stable matching within factors of delta, delta' (respectively) is NP-hard, under strong restrictions. We also give an approximation algorithm for both problems that has a performance guarantee expressible in terms of the number of lists with ties. This significantly improves on the best-known previous performance guarantee, for the case that the ties are sparse. Our results have applications to large-scale centralized matching schemes.

• Item Type: Articles
• Additional Information: Postprint provided by the author
• Keywords: Stable marriage problem; Ties; Unacceptable partners; Inapproximability results; Approximation algorithm
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Manlove, Professor David
• Authors: Halldorsson, M., Irving, R.W., Iwama, K., Manlove, D. F., Miyazaki, S., Morita, Y., and Scott, S.
• Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
• College/School: College of Science and Engineering > School of Computing Science
• Journal Name: Theoretical Computer Science
• Publisher: Elsevier
• ISSN: 0304-3975
• Copyright Holders: ©2003 Elsevier B.V.
• First Published: First published in Theoretical Computer Science306(1-3):431-447
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher.