Electrical flow
Flow minimizing energy (sum of f_e² / c_e). Computable via single Laplacian solve.
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Multiplicative weights
Iteratively adjust edge resistances based on congestion. Converge to max flow.
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Recent: near-linear max flow
Chen-Kyng-Liu-Peng-Gutenberg-Sachdeva 2022: Õ(m^(1+o(1))) max flow. Theoretical breakthrough.
Practical impact
Not yet in production code. Constants large. But theoretical direction of the field.