lect notes-max-flow

lect notes-max-flow - Max Flow In optimal paths, every arc...

Info iconThis preview shows pages 1–13. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Max Flow In optimal paths, every arc has a length, cost, or value. Now, every arc has a width. vi vj bi,j is the amount of flow that can go from vi to vj . 1 / 13 Max Flow 1 1 S 3 1 3 1 1 S 3 1 2 1 1 2 2 T 2 1 2 2 T 2 / 13 Max Matching S T 3 / 13 Ford Fulkerson i max v = ? +v xi,j - xj,k = 0 k -v 0 xi,k bi,k j=s j = s, t j=t 4 / 13 Ford Fulkerson Max flow algorithm X X s t Capacity of a cut: C X, X = iX,jX bi,j 5 / 13 Ford Fulkerson Labeling Process Step 0. vs X Step 1. If vi X and xi,j < bi,j then vj X Step 2. If vi X and xj,i > 0 then vj X 6 / 13 Max Flow a S 3 2 c 2 1 1 1 b 2 2 d 3 T S T 7 / 13 Multi-Terminal Max Flow Undirected edges only. i.e. bi,j = bj,i Given edge capacities j 3 i Result of Max Flows j 7 i 8 7 k 5 4 k 8 / 13 Max Flow For any three nodes, Fi,j , Fj,k , Fi,k satisfy Fi,k min(Fi,j , Fj,k ) X X i k Fi,k = C[ X, X ] 9 / 13 Max Flow Fi,j min(Fi,k , Fk,j ) Fj,k min(Fj,i , Fi,k ) Among any three values, two values must be the same, and the third one is bigger or also the same value. 10 / 13 Max Flow Representation of j 7 i 8 7 k Given n = 100 - node network n 2 Max Flows = (n - 1) Max Flows 11 / 13 Max Flow Edge Capacities e 2 j 3 k 1 1 2 s i Result of Max Flows e 3 j 3 k 2 s i 3 12 / 13 Max Flows For any undirected network, there is a tree-shape network which has the same max flows and the same n - 1 cut value. Gomory-Hu cut tree G - H tree Not only flow - equivalent, but also cut equivalent. 13 / 13 ...
View Full Document

Page1 / 13

lect notes-max-flow - Max Flow In optimal paths, every arc...

This preview shows document pages 1 - 13. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online