Part C project : Stable matchings Supervisor :

The “stable marriage” problem is often described as follows. There are n men and n women; each of the men has an order of preference on the women, and each of the women has an order of preference on the men. A “matching” of the people into n man-woman pairs is said to be unstable if there exist some man and some woman who both prefer each other to their partner in the matching. If there is no such pair, the matching is stable. Does such a stable matching exist? This is a non-trivial question. Gale and Shapley [4] gave an algorithm which finds one. One version is as follows: