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The Stable Matching or the Stable Marriage algorithm is a mathematical algorithm that finds stable matches between two equally sized sets of elements, the proposers and the acceptors.The algorithm works off two independent preference-frames for each set which allows preference based matching to occur.

After the initialization a proposal is made by the proposers to the acceptors and the matching algorithm begins

The solution to the Stable-Matching Problem was first given by David Gale & Lloyd Shapley. The algorithm won Shapley along with Alvin Roth, the 2012 Nobel Memorial Prize in Economic Sciences

The Gale-Shapley algorithm has a wide variety of uses it is used to pair doctors with hospitals, kidneys with patients, employers with trainees, urban students with magnet schools etc.

References :

https://en.wikipedia.org/wiki/Gale%E2%80%93Shapley_algorithmhttps://www.geeksforgeeks.org/stable-marriage-problem/https://www.inc.com/burt-helm/gale-shapley-algorithm-innovation-nobel-prize.html#:~:text=The%20winners%20of%20the%202012,urban%20students%20with%20magnet%20schools.https://towardsdatascience.com/gale-shapley-algorithm-simply-explained-caa344e643c2