Pareto Optimality in House Allocation Problems

  • David J. Abraham
  • Katarína Cechlárová
  • David F. Manlove
  • Kurt Mehlhorn
Conference paper

DOI: 10.1007/978-3-540-30551-4_3

Part of the Lecture Notes in Computer Science book series (LNCS, volume 3341)
Cite this paper as:
Abraham D.J., Cechlárová K., Manlove D.F., Mehlhorn K. (2004) Pareto Optimality in House Allocation Problems. In: Fleischer R., Trippen G. (eds) Algorithms and Computation. ISAAC 2004. Lecture Notes in Computer Science, vol 3341. Springer, Berlin, Heidelberg

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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • David J. Abraham
    • 1
  • Katarína Cechlárová
    • 2
  • David F. Manlove
    • 3
  • Kurt Mehlhorn
    • 4
  1. 1.Computer Science DepartmentCarnegie-Mellon UniversityPittsburghUSA
  2. 2.Institute of MathematicsP.J. Šafárik University in Košice, Faculty of ScienceKošiceSlovakia
  3. 3.Department of Computing ScienceUniversity of GlasgowGlasgowUK
  4. 4.Max-Planck-Institut für InformatikSaarbrückenGermany

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