Stable Marriage Problem

The stable marriage problem is a well-known problem of matching women to men to achieve arncertain type of "stability". Each person expresses a strict preference ordering over the members ofrnthe opposite sex. The goal is to match women and men so that there are no two people of oppositernsex who would both rather be matched with each other than with their current partners. Gale andrnShapley gave an algorithm to solve this problem based on a series of proposals of the women tornthe men (or vice versa). The stable marriage problem has a wide variety of practical applications,rnranging from matching resident doctors to hospitals, job applicants to be assigned by the ministryrnof education, having a living kidney donor as well as in market trading.

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