A 25/17-approximation algorithm for the stable marriage problem with one-sided ties

Authors:
Kazuo Iwama;Shuichi Miyazaki;Hiroki Yanagisawa
Affiliations:
Graduate School of Informatics, Kyoto University;Academic Center for Computing and Media Studies, Kyoto University;IBM Research, Tokyo
Venue:
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part II
Year:
2010

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Abstract

The problem of finding a largest stable matching where preference lists may include ties and unacceptable partners (MAX SMTI) is known to be NP-hard. It cannot be approximated within 33/29 ( 1.1379) unless P=NP, and the current best approximation algorithm achieves the ratio of 1.5. MAX SMTI remains NP-hard even when preference lists of one side do not contain ties, and it cannot be approximated within 21/19 ( 1.1052) unless P=NP. However, even under this restriction, the best known approximation ratio is still 1.5. In this paper, we improve it to 25/17 (