On a generalization of the stable roommates problem

Authors:
Katarína Cechlárová;Tamás Fleiner
Affiliations:
P. J. Šafárik University, Slovakia;Budapest University of Technology and Economics, Hungary
Venue:
ACM Transactions on Algorithms (TALG)
Year:
2005

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Abstract

We consider two generalizations of the stable roommates problem: a) we allow parallel edges in the underlying graph, and b) we study a problem with multiple partners. We reduce both problems to the classical stable roommates problem and describe an extension of Irving's algorithm that solves the generalized problem efficiently. We give a direct proof of a recent result on the structure of stable many-to-many matchings (so called stable b-matchings) as a by-product of the justification of the algorithm.