Lecture23 - Review CSE 421 Algorithms Richard Anderson...

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1 CSE 421 Algorithms Richard Anderson Lecture 23 Network Flow Review • Network flow definitions • Flow examples • Augmenting Paths • Residual Graph • Ford Fulkerson Algorithm •Cu ts • Maxflow-MinCut Theorem Network Flow Definitions • Flowgraph: Directed graph with distinguished vertices s (source) and t (sink) • Capacities on the edges, c(e) >= 0 • Problem, assign flows f(e) to the edges such that: – 0 <= f(e) <= c(e) – Flow is conserved at vertices other than s and t • Flow conservation: flow going into a vertex equals the flow going out – The flow leaving the source is a large as possible Find a maximum flow a s d b c f e g h i t 15 /25 5 /5 20 /20 20 /20 20 /20 25 /30 20 /20 5 /5 20 /20 0 /5 20 /20 15 /20 10 /10 20 /20 5 /5 20 /20 30 /30 0 /5 0 /5 0 /5 0 /5 0 /5 0 /5 0 /20 Residual Graph • Flow graph showing the remaining capacity • Flow graph G, Residual Graph G R – G: edge e from u to v with capacity c and flow f –G R : edge e’ from u to v with capacity c – f R : edge e’’ from v to u with capacity f Augmenting Path Lemma • Let P = v
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This note was uploaded on 02/25/2012 for the course CSE 421 taught by Professor Richardanderson during the Fall '06 term at University of Washington.

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Lecture23 - Review CSE 421 Algorithms Richard Anderson...

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