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

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