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Circulation problems are not just a generalization of max-flow, there is a reduction backwards as well. Suppose we have some directed graph $G = (V, E)$ with edge costs, capacities, and lower bounds. Any edge $u \to v$ in $G$ with we can replace with two nodes $s, t$ and two edges $s \to v$ and $u \to t$ where one of the edges has the original cost, ...


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