On the Maximum Capacity Augmentation Algorithm for the Maximum Flow Problem

Donald Goldfarb, Jianxiu Hao

Abstract: The maximum capacity augmentation algorithm is a variant of the Ford-Fulkerson labeling method in which each flow augmentation is along an augmenting path that yields the maximum increase in flow value. For networks with integer capacities this algorithm has been shown to be polynomial but not to be strongly polynomial, while for networks with real capacities it has been shown that it may require an infinite number of iterations. In this paper, we present two modified versions of the maximum capacity augmentation algorithm which we prove to be strongly polynomial even for real capacities. One of these is a simplex variant.