Newton´s method for fractional combinatorial optimization

The authors considers Newton´s method for the linear fractional combinatorial optimization. He proves a strongly polynomial bound on the number of iterations for the general case. He considers the maximum mean-weight cut problem, which is a special case of the linear fractional combinatorial optimization. This problem is closely related to the parametric flow problem and the flow problem when the maximum arc cost is being minimised. He proves that Newton´s method runs in O(m) iterations for the maximum mean-weight cut problem. One iteration is dominated by the maximum flow computation. This gives the best known strongly polynomial bound of O(m²n) for all three problems mentioned