A new solution for the roommate problem: The Q-stable matchings

The aim of this paper is to propose a new solution for the roommate problem with strict preferences. We introduce the solution of maximum irreversibility and consider almost stable matchings (Abraham et al. [2])and maximum stable matchings (Ta [30] [32]). We find that almost stable matchings are incompatible with the other two solutions. Hence, to solve the roommate problem we propose matchings that lie at the intersection of the maximum irreversible matchings and maximum stable matchings, which are called Q-stable matchings. These matchings are core consistent and we offer an effi cient algorithm for computing one of them. The outcome of the algorithm belongs to an absorbing set.This research is supported by the Spanish Ministry of Science and Innovation (ECO2010- 17049 and ECO2012-31346), co-funded by ERDF, by Basque Government IT-568-13 and by the Government of Andalusia Project for Excellence in Research (P07.SEJ.02547). P eter Bir o also acknowledges the support from the Hungarian Academy of Sciences under its Momentum Programme (LD-004/2010), and the Hungarian Scientific Research Fund,OTKA, grant no.K108673