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A 25/17-Approximation Algorithm for the Stable Marriage Problem with One-Sided Ties

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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 (<1.4706).

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Acknowledgements

The authors would like to thank the anonymous reviewers for their valuable comments.

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Authors and Affiliations

  1. Graduate School of Informatics, Kyoto University, Yoshida-honmachi, Sakyo-ku, Kyoto, 606-8501, Japan

    Kazuo Iwama

  2. Academic Center for Computing and Media Studies, Kyoto University, Yoshida-honmachi, Sakyo-ku, Kyoto, 606-8501, Japan

    Shuichi Miyazaki

  3. IBM Research—Tokyo, NBF Toyosu Canal Front Building, 6-52, Toyosu 5-chome, Koto-ku, Tokyo, 135-8511, Japan

    Hiroki Yanagisawa

Authors
  1. Kazuo Iwama
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  2. Shuichi Miyazaki
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  3. Hiroki Yanagisawa
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Corresponding author

Correspondence to Hiroki Yanagisawa.

Additional information

This work was supported by JSPS KAKENHI Grant Number 22240001, 20700009, 24500013.

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Iwama, K., Miyazaki, S. & Yanagisawa, H. A 25/17-Approximation Algorithm for the Stable Marriage Problem with One-Sided Ties. Algorithmica 68, 758–775 (2014). https://doi.org/10.1007/s00453-012-9699-2

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