Pareto optimality in house allocation problems

Abraham, D.J. and Cechlarova, K. and 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, 20-22 December, 2004, Hong Kong.

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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
Authors:	Abraham, D.J. and Cechlarova, K. and Manlove, D.F. and Mehlhorn, K.
Subjects:	Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Faculty/Department:	Faculty of Information and Mathematical Sciences > Department of Computing Science
Research Group:	Formal Analysis, Theory and Algorithms
Publisher:	Springer Verlag
ISSN:	0302-9743
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.
Related URLs:	Other
Unique ID:	glaseprints:2004-1062
ID Code:	1062
Deposited On:	26 Apr 2005
Last Modified:	05 Dec 2008 12:33

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