A new solution for the roommate problem

Biró, Péter and Inarra, E. and Molis, E. (2014) A new solution for the roommate problem. Műhelytanulmányok = Discussion Papers (MT-DP ). Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences, Budapest. ISBN 978-615-5447-39-6

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Abstract

The aim of this paper is to propose a new solution for the roommate problem with strict references. We introduce the solution of maximum ir reversibility and consider almost stable matchings (Abraham et al. [2]) and maximum stable m atchings (Tan [30] [32]). We find that almost stable matchings are incompatible with the o ther two solutions. Hence, to solve the roommate problem we propose matchings that lie at t he 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 efficient algorithm for computing one of them. The outcome of the algorithm belongs to an ab sorbing set.

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