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The stable marriage problem has been stated as follows: Given n men and n women, where each person has ranked all members of the opposite sex in order of preference, marry the men and women together such that there are no two people of opposite sex who would both rather have each other than their current partners.

When there are no such pairs of people, the set of marriages is deemed stable.

It’s not necessarily too late to rekindle the love with your ex—but don’t get rash and make any mediocre moves. Let her hear your voice and register some sincere effort on your part.

You want to do this right, and that means re-engaging with an abundance of caution and more confidence than ever. “See if she’d like to join you at an art gallery opening, see a movie, or a hike on a sunny day,” says Spira. “If it’s meant to be, she’ll come around on her own time-table.” 4.

Algorithms to solve the hospitals/residents problem can be hospital-oriented (female-optimal) or resident-oriented (male-optimal).

This problem was solved, with an algorithm, in the same original paper by Gale and Shapley, in which the stable marriage problem was solved.

Since such engagements are never stable, all such pairs are deleted and the proposal sequence will be repeated again until either 1) some man's preference list becomes empty (in which case no strongly stable matching exists) or 2) strongly stable matching is obtained.

Upon completion of the algorithm, it is not possible for both Alice and Bob to prefer each other over their current partners.If Alice rejected his proposal, she was already with someone she liked more than Bob.While the solution is stable, it is not necessarily optimal from all individuals' points of view.The traditional form of the algorithm is optimal for the initiator of the proposals and the stable, suitor-optimal solution may or may not be optimal for the reviewer of the proposals.An example is as follows: There are three suitors (A, B, C) and three reviewers (X, Y, Z) which have preferences of: All three are stable because instability requires both participants to be happier with an alternative match.

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