A strongly polynomial-time algorithm for minimizing submodular functions

This paper presents a combinatorial polynomial-time algorithm for minimizing submolular set functions. The algorithm employs a scaling scheme that uses a flow in the complete directed graph on the underlying set with each arc capacity equal to thescaled parameter. The resulting algorithm runs in time bounded by a polynomial in the size of the underlying set and the largest length of the function value. The paper also presents a strongly polynomial-time version that runs in time bounded by a polynomial in the size of the underlying set independent of the function value. These are the first combinatorial algorithms for submodular function minimization that run in (strongly) polynomial time.