Pareto optimality in the Roommates Problem

@inproceedings{Abraham2004ParetoOI,
  title={Pareto optimality in the Roommates Problem},
  author={David J. Abraham and David Manlove},
  year={2004}
}
We consider Pareto optimal matchings as a means of coping with instances of the Stable Roommates problem (SR) that do not admit a stable matching. Given an instance I of SR, we show that the problem of finding a maximum Pareto optimal matching is solvable in O( √ nα(m, n)m log n) time, where n is the number of agents and m is the total length of the preference lists in I. By contrast we prove that the problem of finding a minimum Pareto optimal matching is NP-hard, though approximable within 2… CONTINUE READING

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