doi:10.1016/S0304-3975(03)00319-0 
Copyright © 2003 Elsevier B.V. All rights reserved.
The stable marriage problem with restricted pairs*1
a DCOP, Universidade Estadual de Londrina and COPPE, Universidade Federal do Rio de Janeiro, Brazil
b COPPE, Universidade Federal do Rio de Janeiro, Brazil
c Instituto de Matemática and COPPE, Universidade Federal do Rio de Janeiro, Caixa Postal 68530, 21945-970 Rio de Janeiro, RJ, Brazil
d COPPE, Instituto de Matemática and Núcleo de Computação Eletrônica, Universidade Federal do Rio de Janeiro, Caixa Postal 68511, 21945-970 Rio de Janeiro, RJ, Brazil
Received 15 January 2002;
revised 4 February 2003;
accepted 14 May 2003;
Communicated by G. Ausiello
Available online 11 June 2003.
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Abstract
A stable matching is a complete matching of men and women such that no man and woman who are not partners both prefer each other to their actual partners under the matching. In an instance of the 
problem, each of the n men and n women ranks the members of the opposite sex in order of preference. It is well known that at least one stable matching exists for every
problem instance. We consider extensions of the
problem obtained by forcing and by forbidding sets of pairs. We present a characterization for the existence of a solution for the
problem. In addition, we describe a reduction of the
problem to the
problem. Finally, we also present algorithms for finding a stable matching, all stable pairs and all stable matchings for this extension. The complexities of the proposed algorithms are the same as the best known algorithms for the unrestricted version of the problem.
Author Keywords: Algorithms; Stable marriage; Forced pairs; Forbidden pairs; Rotations
Abstract
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, a, Guilherme D. da Fonseca
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