Xxa Strongly Polynomial - Time Algorithm for Minimizingsubmodular

This paper presents a combinatorial polynomial-time algorithm for minimizing submod-ular set functions. The algorithm employs a scaling scheme that uses a ow in the complete directed graph on the underlying set with each arc capacity equal to the scaled 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 rst combinatorial algorithms for submodular function minimization that run in (strongly) polynomial time.