In mathematics, economics, and computer science, the Gale–Shapley algorithm (also known as the deferred acceptance algorithm or propose-and-reject algorithm) is an algorithm for finding a solution to the stable matching problem, named for David Gale and Lloyd Shapley who had described it as solving both the college admission problem and the stable marriage problem.It takes polynomial time, and the time is linear in the size of the input to the algorithm. It is a truthful mechanism from the point of view of the proposing participants, for whom the solution will always be optimal.