# Lecture23 - CSE 421 Algorithms Richard Anderson Lecture 23...

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CSE 421 Algorithms Richard Anderson Lecture 23 Network Flow

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Review Network flow definitions Flow examples Augmenting Paths Residual Graph Ford Fulkerson Algorithm Cuts 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

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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 – G R : edge e’’ from v to u with capacity f

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Augmenting Path Lemma
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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 - CSE 421 Algorithms Richard Anderson Lecture 23...

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