An efficient cost scaling algorithm for the independent assignment problem

An efficient cost scaling algorithm is presented for the independent assignment problem of Iri and Tomizawa, which is equivalent to the weighted matroid intersection problem of Edmonds. The present algorithm in general can be viewed as a generalization of Orlin and Ahuja's scaling algorithm for the ordinary assignment problem. On a bipartite graph with n vertices and integer arc costs bounded by C, an optimal r- independent assignment can be found in time by our algorithm under an independence oracle for matroids.