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COCOON

2003

Springer

2003

Springer

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 ﬁrst nontrivial result for the approximation with factor less than two. Our randomized algorithm achieves a factor of 10/7 for a restricted but still NP-hard case, where ties occur in only men’s lists, each man writes at most one tie, and the length of ties is two. Furthermore, we show that these restrictions except for the last one can be removed without increasing the approximation ratio too mu...

Related Content

Added |
06 Jul 2010 |

Updated |
06 Jul 2010 |

Type |
Conference |

Year |
2003 |

Where |
COCOON |

Authors |
Magnús M. Halldórsson, Kazuo Iwama, Shuichi Miyazaki, Hiroki Yanagisawa |

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