Abstract
We study Pareto optimal matchings in the context of house allocation problems. We present an \(O(\sqrt{n}m)\) 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.
Due to mistakes during data conversion, this paper was originally published in LNCS 3341 (ISAAC 2004) with several special characters missing in text and figures.
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© 2005 Springer-Verlag Berlin Heidelberg
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Abraham, D.J., Cechlárová, K., Manlove, D.F., Mehlhorn, K. (2005). Pareto Optimality in House Allocation Problems. In: Deng, X., Du, DZ. (eds) Algorithms and Computation. ISAAC 2005. Lecture Notes in Computer Science, vol 3827. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11602613_115
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DOI: https://doi.org/10.1007/11602613_115
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-30935-2
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