Lecture22 - Network Flow CSE 421 Algorithms Richard...

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1 CSE 421 Algorithms Richard Anderson Lecture 22 Network Flow Network Flow Outline • Network flow definitions • Flow examples • Augmenting Paths • Residual Graph • Ford Fulkerson Algorithm •Cu ts • Maxflow-MinCut Theorem Network Flow Definitions • Capacity • Source, Sink • Capacity Condition • Conservation Condition • Value of a flow Flow Example u s t v 20 20 30 10 10 Flow assignment and the residual graph u s t v 15/20 20/20 15/30 0/10 5/10 u s t v 5 15 10 5 20 15 15
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2 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 Flow Example a s d b c f e g h i t 20 5 20 20 20 20 20 5 5 5 20 5 10 20 5 20 20 5 20 20 5 5 10
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Lecture22 - Network Flow CSE 421 Algorithms Richard...

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