Maximum Flow digraph:D(V,E) source:s sink:t capacity:c:E→&+ max ∑f u:(s,u)∈E s.t.0≤fuv≤Cu ∀(u,v)∈E ∑fww-∑fu=0 u∈V\{s,t} w:(w,u)∈E w:(u,v)∈E integral flow:fuu∈Z (u,v)∈E
Maximum Flow digraph: D(V,E) capacity: source: s sink: t max u:(s,u)E fsu ⇥(u, v) E ⇥u V \ {s, t} w:(w,u)E fwu v:(u,v)E fuv = 0 s.t. 0 fuv cuv c : E R+ Z+ integral flow: fuv Z ⇥(u, v) E
Cut digraph:D(V,E) source:s sink:t capacity:c:E→R+ 0/1 0/1 0/1 0/1 0/3 0/3 0/4 0/1 0/1 s-t cut; SCV Cuv s∈S,ttS u∈S,vtS,(u,w)∈E
Cut digraph: D(V,E) capacity: c : E R+ 0/1 0/4 0/1 0/1 0/1 0/1 0/1 0/4 0/3 0/3 s t source: s sink: t uS,v⇥S,(u,v)E s-t cut: cuv s S, t ⇥ S S V