An extendable stable matching algorithm of a kind of bipartite graph

Real-life examples of assignment problems, like college admission, the labor market for medical interns, and sorority rush, can be formulated as bipartite matching. The college admission problem is one of many-to-one matching in two-sided matching models. We can obtain a bipartite graph by viewing all colleges and students as two disjointed sets of vertices, and joining an edge between their corresponding vertices, if the student enrolled this college. Thus, the college admission problem can be formulated as finding a stable extensive matching in the corresponding bipartite graph. In this paper, by using the definition of the stable extensive matching, we give an algorithm with O(m3n3) for the college admission problem, which is different from the Gale and Shapley algorithm. Moreover, the algorithm can be viewed as a generalization of Hungarian Algorithm.