Pareto optimality in house allocation problems

Abraham, D.J., Cechlarova, K., Manlove, D.F. and Mehlhorn, K. (2004) Pareto optimality in house allocation problems. In: Proceedings of ISAAC 2004: the 15th Annual International Symposium on Algorithms and Computation, Hong Kong, 20-22 December, 2004, pp. 3-15. ISBN 3-540-24131-0

Abstract

We study Pareto optimal matchings in the context of house allocation problems. We present an O(\sqrt{n}m) algorithm, based on Gales Top Trading Cycles Method, for finding a maximum cardinality Pareto optimal matching, where n is the number of agents and m is the total length of the preference lists. By contrast, we show that the problem of finding a minimum cardinality Pareto optimal matching is NP-hard, though approximable within a factor of 2. We then show that there exist Pareto optimal matchings of all sizes between a minimum and maximum cardinality Pareto optimal matching. Finally, we introduce the concept of a signature, which allows us to give a characterization, checkable in linear time, of instances that admit a unique Pareto optimal matching.

• Item Type: Conference Proceedings
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Manlove, Professor David
• Authors: Abraham, D.J., Cechlarova, K., Manlove, D.F., and Mehlhorn, K.
• 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: 3-540-24131-0
• Copyright Holders: © Springer-Verlag
• First Published: First published in the Lecture Notes in Computer Science 3341:3-15
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher.

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