# Pareto optimality in the Roommates Problem

@inproceedings{Abraham2004ParetoOI, title={Pareto optimality in the Roommates Problem}, author={David J. Abraham and David Manlove}, year={2004} }

- Published 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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#### References

##### Publications referenced by this paper.

Showing 1-10 of 23 references

## On the complexity of exchange-stable roommates

View 14 Excerpts

Highly Influenced

## Pareto Optimality in House Allocation Problems

View 1 Excerpt

## The exchange-stable marriage problem

View 14 Excerpts

## An empirical study of the stable roommates problem

View 1 Excerpt

## The Stable Roommates Problem with Ties

View 1 Excerpt

## Unique Maximum Matching Algorithms

View 1 Excerpt

## Stable Marriage and its Relation to Other Combinatorial Problems, volume 10 of CRM Proceedings and Lecture Notes

View 1 Excerpt

## Exchance-proofness or divorce-proofness? Stability in one-sided matching markets

View 2 Excerpts

## Generalizing NP-completeness proofs for bipartite and chordal graphs

View 1 Excerpt