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Stable matching and the marriage problem
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Abstract
In this investigation the Stable Marriage Problem is presented which
seeks to find the appropriate match between men and women, but taking into
account the preference list that each person express his preference to
members of the opposite sex. This match is based on the stability of the
solution, that is, an already matched couple does not have the incentive to leave
its existing choice. At the same time, information on the termination and stability
of the solution is presented. Furthermore, the uniqueness of the solution is
highlighted along with the lack of justice of the solution to the members of the
set l that they do not propose but are in place to accept the proposals of the
members of the other set. Additionally, various variations of the Gale & Shapley
algorithm are presented, such as non-full preference lists, preference lists, the
combination of problems with non-complete preference lists and equality lists,
hospital and residence problem and the student's pairing problem in two person rooms.