Shortest_Augmenting_Path

# Shortest_Augmenting_Path - The Shortest Augmenting Path...

This preview shows pages 1–8. Sign up to view the full content.

The Shortest Augmenting Path Algorithm for the Maximum Flow Problem

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

View Full Document
2 Shortest Augmenting Path 4 1 4 1 2 3 1 s 2 5 3 t This is the original network, plus reversals of the arcs.
3 Shortest Augmenting Path 4 1 1 4 1 2 3 1 s 2 5 3 t This is the original network, and the original residual network.

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

View Full Document
4 Initialize Distances 4 1 1 4 1 2 3 1 The node label henceforth will be the distance label. 0 5 4 3 2 1 t 4 5 3 s 2 d(j) is at most the distance of j to t in G(x) 0 2 2 1 1 1
5 Representation of admissible arcs 4 1 1 4 1 2 3 1 An arc (i,j) is admissible if d(i) = d(j) + 1. 0 5 4 3 2 1 t 4 5 3 s 2 An s-t path of admissible arcs is a shortest path 0 2 2 1 1 Admissible arcs will be represented with thick lines

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

View Full Document
6 4 2 Look for a shortest s-t path 4 1 1 1 3 1 Start with s and do a depth first search using admissible arcs. 0 5 4 3 2 1 t 4 5 3 s 2 2 1 1 Next. Send flow, and update the residual capacities. 2 1 0
7 4 2 2 Update residual capacities 4 1 1 1 3 3 1 Here are the updated residual capacities. 0

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 04/15/2010 for the course INDUSTRIAL ie513 taught by Professor Zeynephuygur during the Spring '10 term at Bilkent University.

### Page1 / 22

Shortest_Augmenting_Path - The Shortest Augmenting Path...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online