Question: A given flow network G may have more than one minimum (s, t)-cut. While all minimum (s, t)-cuts will have the same capacity, they may

A given flow network G may have more than one minimum (s, t)-cut. While all minimum (s, t)-cuts will have the same capacity, they may have different numbers of edges directed from the s side to the t side. Let us define the best minimum (s, t)-cut to be any minimum cut with the smallest number of edges crossing the cut directed from the s side to the t side of the cut. (When the minimum cut is unique, by default it is also the best.) Describe and analyze an efficient algorithm to find the best minimum (s, t)-cut in a given flow network with integral capacities. (You may use as a subroutine an efficient max-flow algorithm without describing it in detail.)

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