Min Cost Flow

Network with Cost

Residual Graph: backward edges have negative cost

Transclude of AA-cost-network-note.excalidraw

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Circulation

typo: $f_i$ is a circulation in $\mathcal{N}$ for all $i\in [k]$ and …

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Optimality

Generic Cycle-Canceling Algorithm
Minimum-Mean Cycle Algorithm

Minimum-Cost Flow as LP