Why it matters

Solves many optimization problems by reduction. Understanding shapes flow algorithms.

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The architecture

Flow network: capacities on edges.

Cut: partition (S, T) with s in S, t in T.

Min-cut max-flowSource sflow originCut (S, T)partition edgesSink tflow destinationAny max flow saturates a min cut; residual graph reveals cut
Max-flow min-cut.
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How it works end to end

Residual graph: reveals augmenting paths.

When no path exists, flow is max.

Reachable from s = S; rest = T.

Cut edges saturated.