Compute an optimal solution to the global

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n the (undirected) global minimum cut problem, the input is an undirected graph G = (V, E) with a nonnegative capacity ue for each edge e ∈ E, and the goal is to identify a cut (A, B) - i.e., a partition of V into non-empty sets A and B - that minimizes the total capacity ∑ e∈δ(S) ue of the cut edges. (Here, δ(A) denotes the edges with exactly one endpoint in A.)

Prove that this problem reduces to solving n - 1 minimum s-t cut problems. That is, given an instance of the global minimum cut problem, show how to (i) produce n - 1 instances of the minimum s-t cut problem (as described in lecture) such that (ii) given minimum s-t cuts to these n - 1 instances, you can compute an optimal solution to the global minimum cut instance. Your implementations of steps (i) and (ii) should run in polynomial time. Include a brief proof of correctness

Reference no: EM133626094

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