The stable matching problem/algorithm attempts to find a stable matching (pairing) between individuals of two sets of the same size given a ranking of preferences for each individual within the set. A matching is a mapping from the elements of one set to the elements of the other set.

The matching is said to be unstable if:
a) There is an element A of the first matched set which prefers some given element B of the second matched set over the element to which A is already matched, and
b) B also prefers A over the element to which B is already matched

The matching is said to be stable if:
There does not exist any match (A, B) in which both A and/or B would be individually better off than they are with their current match.

The most useful applications of this problem include hospital-resident assignments, roommate assignments, and even in sorority rush processes. Although the stable marriage problem is useful in the field of computer science, it is not all that practical in the real world. It has been proven that whomever (man or woman) proposes will end up with their best possible match, and whomever is proposed to will end up with their worst possible match.