A combinatorial algorithm minimizing submodular functions in strongly polynomial time

We give a strongly polynomial-time algorithm minimizing a submodular function f given by a value-giving oracle. The algorithm does not use the ellipsoid method or any other linear programming method. No bound on the complexity of the values of f is needed lo be known a priori. The number of oracle calls is bounded by a polynomial in the size of the underlying set. (C) 2000 Academic Press.