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Improved Approximation of the Stable Marriage Problem

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Algorithms - ESA 2003 (ESA 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2832))

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Abstract

The stable marriage problem has recently been studied in its general setting, where both ties and incomplete lists are allowed. It is NP-hard to find a stable matching of maximum size, while any stable matching is a maximal matching and thus trivially a factor two approximation.

In this paper, we give the first nontrivial result for approximation of factor less than two. Our algorithm achieves an approximation ratio of 2/(1+L − 2) for instances in which only men have ties of length at most L. When both men and women are allowed to have ties, we show a ratio of 13/7(< 1.858) for the case when ties are of length two. We also improve the lower bound on the approximation ratio to \(\frac{21}{19}\)(> 1.1052).

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Iceland, Iceland

    Magnús M. Halldórsson

  2. Graduate School of Informatics, Kyoto University, Japan

    Kazuo Iwama & Hiroki Yanagisawa

  3. Academic Center for Computing and Media Studies, Kyoto University, Japan

    Shuichi Miyazaki

Authors
  1. Magnús M. Halldórsson
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  2. Kazuo Iwama
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  3. Shuichi Miyazaki
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  4. Hiroki Yanagisawa
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Editor information

Editors and Affiliations

  1. Dipartimento di Informatica e Automazione, Università degli Studi “Roma Tre”, via della Vasca Navale 79, 00146, Rome, Italy

    Giuseppe Di Battista

  2. School of Computer Science, Tel Aviv University, 69978, Tel Aviv, Israel

    Uri Zwick

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© 2003 Springer-Verlag Berlin Heidelberg

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Halldórsson, M.M., Iwama, K., Miyazaki, S., Yanagisawa, H. (2003). Improved Approximation of the Stable Marriage Problem. In: Di Battista, G., Zwick, U. (eds) Algorithms - ESA 2003. ESA 2003. Lecture Notes in Computer Science, vol 2832. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39658-1_26

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  • DOI: https://doi.org/10.1007/978-3-540-39658-1_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20064-2

  • Online ISBN: 978-3-540-39658-1

  • eBook Packages: Springer Book Archive

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