Question: Let G = (V, E) be a flow network in which every edge has capacity 1 and the shortest-path distance from s to t is

Let G = (V, E) be a flow network in which every edge has capacity 1 and the shortest-path distance from s to t is at least d. (a) Prove that the value of the maximum (s,t)-flows is at most E/d.

(b) Now suppose that G is simple, meaning that for all vertices u and v, there is at most one edge from u to v. Prove that the value of the maximum (s, t)-flow is at most O(V^ 2/d^2).

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