Let G = (V, E) be a flow network with source s and sink t. We say that an edge e is a bottleneck if it crosses every minimum-capacity cut separating s from t. Give an efficient algorithm to determine...

Let G = (V, E) be a flow network with source s and sink t. We say that an edge e is a bottleneck if it crosses every minimum-capacity cut separating s from t. Give an efficient algorithm to determine if a given edge e is a bottleneck in G. Analyze the running time of your algorithm.