The complexity of counting stable marriages
SIAM Journal on Computing
An efficient algorithm for the “optimal” stable marriage
Journal of the ACM (JACM)
The stable marriage problem: structure and algorithms
The stable marriage problem: structure and algorithms
Many-to-many matching: stable polyandrous polygamy (or polygamous polyandry)
Discrete Applied Mathematics
Communications of the ACM
A unified approach to finding good stable matchings in the hospitals/residents setting
Theoretical Computer Science
Rotations in the stable b-matching problem
Theoretical Computer Science
Finding All Stable Pairs and Solutions to the Many-to-Many Stable Matching Problem
INFORMS Journal on Computing
Note: Blockers and antiblockers of stable matchings
Theoretical Computer Science
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This paper considers the many-to-many version of the stable marriage problem where each man and woman has a strict preference ordering on the members of the opposite sex that he or she considers acceptable. Further, each man and woman wishes to be matched to as many acceptable partners as possible, up to his or her specified quota. In this setup, a polynomial time algorithm for finding a stable matching that minimizes the sum of partner ranks across all men and women is provided. It is argued that this sum can be used as an optimality criterion for minimizing total dissatisfaction if the preferences over partner-combinations satisfy a no-complementarities condition. The results in this paper extend those already known for the one-to-one version of the problem.