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# Minimum Cut ( min_cut )

A cut C in a network is a set of nodes that is neither empty nor the entire set of nodes. The weight of a cut is the sum of the weights of the edges having exactly one endpoint in C.

 int MIN_CUT(const graph& G, const edge_array& weight, list& C, bool use_heuristic = true) MIN_CUT takes a graph G and an edge_array weight that gives for each edge a non-negative integer weight. The algorithm ([82]) computes a cut of minimum weight. A cut of minimum weight is returned in C and the value of the cut is the return value of the function. The running time is O(nm + n2log n). The function uses a heuristic to speed up its computation. Precondition The edge weights are non-negative. list MIN_CUT(const graph& G, const edge_array& weight) as above, but the cut C is returned. int CUT_VALUE(const graph& G, const edge_array& weight, const list& C) returns the value of the cut C.

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