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Unformatted text preview: And its bounded above by Cap({s}). So # iterations is bounded. (2) F.F. computes a feasible ow. Induction on # of iterations. Flow values remain between 0 and c e because bottleneck(P,f) was dened so that f(e) is between 0 and c e . Flow convervation 183 (3) f is a maximum Fow. If we can nd (A, A ) such that Cap(A) = v(f) we are done, because for every other Fow f v(f ) Cap(A) = v(f) 184 Let A = {vertices reachable from s in G f } Notice that s A, t A. Every edge in E(A, A ) is saturated, f(e) = c e . Recall: For every ow f, v(f) = f(e)  f(e) e Out(A) e In(A) = f(e) + (f(e)  f(e))  f(e) e E(A,A ) e E(A,A) e E(A ,A) = c e f(e) = Cap(A) e E(A,A ) e E(A ,A) 185...
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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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