Randomized approximation of the stable marriage problem

  • Authors:

  • Magnús M. Halldórsson;Kazuo Iwama;Shuichi Miyazaki;Hiroki Yanagisawa

  • Affiliations:

  • Department of Computer Science, University of Iceland, IS-107 Reykjavik, Iceland;Graduate School of Informatics, Kyoto University, Yoshida-honmachi, Sakyo-ku, Kyoto 606-8501, Japan;Academic Center for Computing and Media Studies, Kyoto University, Yoshida-honmachi, Sakyo-ku, Kyoto 606-8501, Japan;IBM Tokyo Research Laboratory, 1623-14 Shimotsuruma, Yamato-shi, Kanagawa-ken, 242-8502, Japan and Graduate School of Informatics, Kyoto University, Yoshida-honmachi, Sakyo-ku, Kyoto 606-8501, Jap ...

  • Venue:
  • Theoretical Computer Science - Special papers from: COCOON 2003
  • Year:
  • 2004

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Abstract

While the original stable marriage problem requires all participants to rank all members of the opposite sex in a strict order, two natural variations are to allow for incomplete preference lists and ties in the preferences. Either variation is polynomially solvable, but it has recently been shown to be NP-hard to find a maximum cardinality stable matching when both of the variations are allowed. It is easy to see that the size of any two stable matchings differ by at most a factor of two, and so, an approximation algorithm with a factor two is trivial. In this paper, we give a randomized approximation algorithm RANDBRK and show that its expected approximation ratio is at most 10/7 (