UNIVERSITY of GLASGOW

Computing at Glasgow University
 
Paper ID: 6985

Approximability results for stable marriage problems with ties
Halldorsson,M.M. Irving,R.W. Iwama,K. Manlove,D.F. Miyazaki,S. Morita,Y. Scott,S.

Publication Type: Journal
Appeared in: Theoretical Computer Science, volume 306
Page Numbers : 431-447
Publisher: Elsevier Science
Year: 2003
ISBN/ISSN: 0304-3975

URL: This publication is available at this URL.

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 d,d' such that each of the problems of approximating a maximum and minimum cardinality stable matching within factors of d,d' (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.

Keywords: Stable marriage problem; Ties; Unacceptable partners; Inapproximability results; Approximation algorithm


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