The stable matching problem attempts to find a stable matching (pairing) between 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