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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)

Weakly and strongly polynomial algorithms for computing the maximum decrease in uniform arc capacities