The stable marriage problem: structure and algorithms
The stable marriage problem: structure and algorithms
Matching Medical Students to Pairs of Hospitals: A New Variation on a Well-Known Theme
ESA '98 Proceedings of the 6th Annual European Symposium on Algorithms
A 3/2-Approximation Algorithm for General Stable Marriage
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Social Networks and Stable Matchings in the Job Market
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Size versus stability in the marriage problem
Theoretical Computer Science
Local matching dynamics in social networks
Information and Computation
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In the Hospitals/Residents (HR) problem, agents are partitioned into hospitals and residents. Each agent wishes to be matched to an agent (or agents) in the other set and has a strict preference over these potential matches. A matching is stable if there are no blocking pairs, i.e., no pair of agents that prefer each other to their assigned matches. Such a situation is undesirable as it could lead to a deviation in which the blocking pair form a private arrangement outside the matching. This however assumes that the blocking pair have social ties or communication channels to facilitate the deviation. Relaxing the stability definition to take account of the potential lack of social ties between agents can yield larger stable matchings. In this paper, we define the Hospitals/Residents problem under Social Stability (HRSS) which takes into account social ties between agents by introducing a social network graph to the HR problem. Edges in the social network graph correspond to resident-hospital pairs in the HR instance that know one another. Pairs that do not have corresponding edges in the social network graph can belong to a matching M but they can never block M. Relative to a relaxed stability definition for HRSS, called social stability, we show that socially stable matchings can have different sizes and the problem of finding a maximum socially stable matching is NP-hard, though approximable within 3/2. Furthermore we give polynomial time algorithms for special cases of the problem.