Abstract
AbstractThe stable marriage problem (SM) and the Hospital / Residents problem (HR) are both stable matching problems. They consist of two sets of objects that need to be matched to each other; in SM men to women, and in HR residents to hospitals. Each set of objects expresses a ranked preference for the objects in the other set, in the form of a preference list. The problem is then to find a matching of one set to the other such that the matching is stable. A matching is stable iff it contains no blocking pairs. A blocking pair in a matching M consists of two objects x and y one from each set(x = man and y = woman for SM or x = hospital and y = resident in HR), such that x and y are not matched in M and both x and y would rather be matched to each other than to there assignment in M.
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