# Lecture23 - Review CSE 421 Algorithms Richard Anderson...

This preview shows pages 1–2. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## 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.

### Page1 / 3

Lecture23 - Review CSE 421 Algorithms Richard Anderson...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online