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Network flow

Take network G=(V,E) with source s, sink t; \ $(u,v) \in E$ has capacity c(u,v). Flow $f:V\times V \to R$ with capacity constraints, flow conservation $\sum_{u} f(u, v) = 0$, skew symmetry: f(u, v) = -f(v, u). Residual capacity of an edge: $c_{f}(u, v)$. Thence, can get residual network $G_{f}$. Augmenting path $s, v_{1}, v_{2} .. t$: $\forall i, c_{f}(v_{i}, v_{i+1})>0$.

Max flow problem

Start with 0 flow. Max flow exists iff $ \nexists $ augmenting path. Check for augmented flow; Keep increasing or decreasing flow by small fractions.

Min cut problem

Reduce to max flow problem.