In this paper, a new problem on a directed network is presented. Let D be a
feasible network such that all arc capacities are equal to U. Given a t > 0,
the network D with arc capacities U - t is called the t-network. The goal of
the problem is to compute the largest t such that the t-network is feasible.
First, we present a weakly polynomial time algorithm to solve this problem,
which runs in O(log(nU)) maximum flow computations, where n is the number of
nodes. Then, an O(m2n) time approach is presented, where m is the number of
arcs. Both the weakly and strongly polynomial algorithms are inspired by
McCormick and Ervolina (1994).