Stable Marriage with Incomplete Lists and Ties
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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 N 1-∈ , where N is the instance size, unless P=NP.
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- Stable Marriage with Incomplete Lists and Ties
- Book Title
- Automata, Languages and Programming
- Book Subtitle
- 26th International Colloquium, ICALP’99 Prague, Czech Republic, July 11–15, 1999 Proceedings
- pp 443-452
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- Series Title
- Lecture Notes in Computer Science
- Series Volume
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- Springer Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
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- Editor Affiliations
- 4. Institute for Computer Science, Academy of Sciences of the Czech Republic
- 5. ILLC-WINS-University of Amsterdam
- 6. BRICS, Department of Computer Science, University of Aarhus
- Author Affiliations
- 7. School of Informatics, Kyoto University, Kyoto, 606-8501, Japan
- 8. Dept. of Computing Science, University of Glasgow, Glasgow, G12 8QQ, Scotland
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