A matching is not stable if: In other words, a matching is stable when there does not exist any match (A, B) by which both A and B would be individually better off than they are with the element to which they are currently matched.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. build(); var inline_leaderboard_mapping = Mapping().).
In mathematics, economics, and computer science, the stable marriage problem (also stable matching problem or SMP) is the problem of finding a stable matching between two equally sized sets of elements given an ordering of preferences for each element.
A matching is a mapping from the elements of one set to the elements of the other set.
Upon completion of the algorithm, it is not possible for both Alice and Bob to prefer each other over their current partners.]]
Content delivery networks that distribute much of the world's content and services solve this large and complex stable marriage problem between users and servers every tens of seconds to enable billions of users to be matched up with their respective servers that can provide the requested web pages, videos, or other services.Giving everyone their second choice ensures that any other match would be disliked by one of the parties.The algorithm converges in a single round on the suitor-optimal solution because each reviewer receives exactly one proposal, and therefore selects that proposal as its best choice, ensuring that each suitor has an accepted offer, ending the match.This asymmetry of optimality is driven by the fact that the suitors have the entire set to choose from, but reviewers choose between a limited subset of the suitors at any one time.In the classical version of the problem, each person must rank the members of the opposite sex in strict order of preference.