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) by in which both A and/or B would be individually better off than they are with their current match.