This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: And it’s 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 de²ned 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...
View
Full Document
 Spring '08
 KLEINBERG
 Algorithms, #, Flow network, Maximum flow problem, Maxflow mincut theorem, Network flow

Click to edit the document details