An O(n^3) time algorithm for the maximum weight b-matching problem on bipartite graphs

Abstract: Given an undirected bipartite graph G= (A U B,E), the b-matching of G matches each vertex v in A (B) to at least 1 and at most b(v) vertices in B (A), where b(v) denotes the capacity of v. In this paper, we present an O(n^3) time algorithm for finding a maximum weight b-matching of G, where |A|+|B|=O(n). Our algorithm improves the previous best time complexity of O(n^3 log n) for this problem.