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Unformatted text preview: such that s A, t A . The capacity of a cut is Cap(A) = c e e=(u,v) u A, v A Lemma: If G is a Fow network, f is a Fow, A, A is a cut, then v(f) = Cap(A). Proof. v(f) = f(e) = f(e)  f(e) e Out(s) e Out(A) e In(A) = (f(e)  f(e)) + f(e)  f(e) e Out(A) In(A) e Out(A)\In(A) e out(A)\In(A) f(e) e Out(A)\In(A) c e = Cap(A) e Out(A)\In(A) Cap(A) = c e e = (u,v) u A, v A 173 Def: Given a Fow network G and a Fow f, the residual graph G f has vertex set V, edge set E f = E {(v,u)  edge e (u,v) has Fow > 0} 174 Capacities are c e f(e) if e is in G f( < e ) if < e is in G e = (u,v) < e = (v,u) 175...
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This note was uploaded on 10/02/2008 for the course CS 482 taught by Professor Kleinberg during the Spring '08 term at Cornell University (Engineering School).
 Spring '08
 KLEINBERG
 Algorithms

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