Chapter 11 Min Cut

x To acknowledge the corn-This purely American expression means to admit the losing of an argument , especially in regard to a detail; to retract; to admit defeat. It is over a hundred years old. Andrew Stewart, a member of Congress, is said to have mentioned it in a speech in 1828. He said that haystacks and cornfields were sent by Indiana, Ohio and Kentucky to Philadelphia and New York. Charles A. Wickliffe, a member from Kentucky questioned the statement by commenting that haystacks and corn-fields could not walk. Stewart then pointed out that he did not mean literal haystacks and cornfields, but the horses, mules, and hogs for which the hay and corn were raised. Wickliffe then rose to his feet, and said, "Mr. Speaker, I acknowledge the corn". Let G = (V, E) be undirected graph with n vertices and m edges. We are interested in cuts in G. where S ∅ and V \ S ∅. We will refer to the number of edges in the cut (S , V \ S) as the size of the cut. For an example of a cut, see figure on the right. We are interested in the problem of computing the minimum cut (i.e., mincut), that is, the cut in the graph with minimum cardinality. Specifically, we would like to find the set S ⊆ V such that (S , V \ S) is as small as possible, and S is neither empty nor V \ S is empty.