Pareto Optimality in House Allocation Problems

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Pareto Optimality in House Allocation Problems
We study Pareto optimal matchings in the context of house allocation problems. We present an O( √ nm) algorithm, based on Gale’s 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.
David J. Abraham, Katarína Cechlárov
Added 02 Jul 2010
Updated 02 Jul 2010
Type Conference
Year 2004
Authors David J. Abraham, Katarína Cechlárová, David Manlove, Kurt Mehlhorn
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