# Lecture22 - CSE 421 Algorithms Richard Anderson Lecture 22...

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CSE 421 Algorithms Richard Anderson Lecture 22 Network Flow

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Network Flow
Outline Network flow definitions Flow examples Augmenting Paths Residual Graph Ford Fulkerson Algorithm Cuts Maxflow-MinCut Theorem

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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

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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 5
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

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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 30
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Lecture22 - CSE 421 Algorithms Richard Anderson Lecture 22...

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