Stable marriage with incomplete lists and ties

Iwama, K., Manlove, D.F. , Miyazaki, S. and Morita, Y. (1999) Stable marriage with incomplete lists and ties. In: Proceedings of ICALP '99: the 26th International Colloquium on Automata, Languages and Programming, Prague, Czech Republic, 11-15 July, 1999, pp. 443-452. ISBN 3-540-66224-3

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 N^{1-epsilon}, where N is the instance size, unless P=NP.

• Item Type: Conference Proceedings
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Manlove, Professor David
• Authors: Iwama, K., Manlove, D.F., Miyazaki, S., and Morita, Y.
• Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
• College/School: College of Science and Engineering > School of Computing Science
• Research Group: Formal Analysis, Theory and Algorithms
• Publisher: Springer Verlag
• ISSN: 0302-9743
• ISBN: 3-540-66224-3
• Copyright Holders: © Springer-Verlag
• First Published: First published in Lecture Notes in Computer Science 1644:443-452
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher.