Abstract
The original stable marriage problem requires all men and women to submit a complete and strictly ordered preference list. This is obviously often unrealistic in practice, and several relaxations have been proposed, including the following two common ones: one is to allow an incomplete list, i.e., a man is permitted to accept only a subset of the women and vice versa. The other is to allow a preference list including ties. Fortunately, it is known that both relaxed problems can still be solved in polynomial time. In this paper, we show that the situation changes substantially if we allow both relaxations (incomplete lists and ties) at the same time: the problem not only becomes NP-hard, but also the optimal cost version has no approximation algorithm achieving the approximation ratio of N1-∈, where N is the instance size, unless P=NP.
Supported in part by Scientific Research Grant, Ministry of Japan, 10558044, 09480055 and 10205215.
Supported by Engineering and Physical Sciences Research Council grant number GR/M13329.
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© 1999 Springer-Verlag Berlin Heidelberg
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Iwama, K., Manlove, D., Miyazaki, S., Morita, Y. (1999). Stable Marriage with Incomplete Lists and Ties. In: Wiedermann, J., van Emde Boas, P., Nielsen, M. (eds) Automata, Languages and Programming. Lecture Notes in Computer Science, vol 1644. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48523-6_41
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DOI: https://doi.org/10.1007/3-540-48523-6_41
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