Consider the following problem. You are given a flow network with unit- capacity edges: It consists of a directed graph G = (V, E), a source s V, and a sink t V; and ce = 1 for every e E. You are also given a parameter k.

The goal is to delete k edges so as to reduce the maximum s-t flow in G by as much as possible. In other words, you should find a set of edges F E so that |F| = k and the maximum s-t flow in G = (V, E F) is as small as possible subject to this. Give a polynomial-time algorithm to solve this problem.