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A ( \(2-c\frac{1}{\sqrt{N}}\) )-Approximation Algorithm for the Stable Marriage Problem

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Abstract

We consider the problem of finding a stable matching of maximum size when both ties and unacceptable partners are allowed in preference lists. This problem is NP-hard and the current best known approximation algorithm achieves the approximation ratio 2−c(log N)/N, where c is an arbitrary positive constant and N is the number of men in an input. In this paper, we improve the ratio to \(2-c/\sqrt{N}\) , where c is an arbitrary constant that satisfies \(c\leq 1/{(4\sqrt{6})}\) .

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Authors and Affiliations

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

    Kazuo Iwama & Naoya Yamauchi

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

    Shuichi Miyazaki

Authors
  1. Kazuo Iwama
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  2. Shuichi Miyazaki
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  3. Naoya Yamauchi
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Corresponding author

Correspondence to Shuichi Miyazaki.

Additional information

A preliminary version of this paper was presented at the 16th Annual International Symposium on Algorithms and Computation, ISAAC 2005.

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Iwama, K., Miyazaki, S. & Yamauchi, N. A ( \(2-c\frac{1}{\sqrt{N}}\) )-Approximation Algorithm for the Stable Marriage Problem. Algorithmica 51, 342–356 (2008). https://doi.org/10.1007/s00453-007-9101-y

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