Suppose you are given a directed graph G = (V, E), with a positive integer capacity ce on each edge e, a source s e V, and a sink t e V. You are also given a maximum s-t flow in G, defined by a flow value fe on each edge e. The flow f is acyclic: There is no cycle in G on which all edges carry positive flow. The flow f is also integer-valued.
Now suppose we pick a specific edge e* ε E and reduce its capacity by 1 unit. Show how to find a maximum flow in the resulting capacitated graph in time O(m +n), where m is the number of edges in G and n is the number of nodes.
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