A descent method for submodular function minimization

We show a descent method for submodular function minimization based on an oracle for membership in base polyhedra. We assume that for any submodular function f : D --> R on a distributive lattice D subset of or equal to 2(V) with theta, V is an element of D and f(theta) = 0 and for any vector x is an element of R-V where V is a finite nonempty set. the membership oracle answers whether x belongs to the base polyhedron associated with f and that if the answer is NO, it also gives us a set Z is an element of D such that x(Z) > f(Z), Given a submodular function f, by invoking the membership oracle O(\V\(2)) times, the descent method finds a sequence of subsets Z(1), Z(2).....Z(k) of V such that f(Z(1)) > f(Z(2)) > (...) > f(Z(k)) = min{f(Y) \ Y is an element of D}, where k is O(\V\(2)). The method furnishes an alternative framework for submodular function minimization if combined with possible efficient membership algorithms.