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(Duality and the Max-Flow/Min-Cut Theorem) Consider a feasible max-flow problem and let Q = [S, N -S] be a minimum capacity cut separating s and t. Consider also the minimum cost flow problem formulation for the max-flow problem Show that the price vector

1345_3deb28e8-e238-4ea3-b4a0-42f5d2d27ac0.png

is an optimal solution of the dual problem. Furthermore, show that the max- flow/min-cut theorem expresses the equality of the primal and dual optimal costs.

Computer Engineering, Engineering

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