7 FordFulkerson Demo Algorithm Design by va Tardos

7. Ford-Fulkerson Demo Algorithm Design by Éva Tardos and Jon Kleinberg • Copyright © 2005 Addison Wesley • Slides by Kevin Wayne

Ford-Fulkerson Algorithm G: 0 10 s 0 10 2 0 4 2 0 0 8 3 0 9 4 60 0 10 5 0 10 flow capacity t Flow value = 0 2

Ford-Fulkerson Algorithm G: 8 X 0 10 s 0 10 2 0 4 2 0 0 8 X 8 3 0 9 4 60 5 0 10 8 X 0 10 flow capacity t 8 Flow value = 0 2 4 4 2 8 6 10 3 9 5 10 Gf : 10 s 10 residual capacity t 3

Ford-Fulkerson Algorithm 2 G: 10 X 8 10 0 10 s 2 X 0 2 3 0 4 8 8 0 2 X 9 4 60 5 0 10 8 10 X 10 t 10 Flow value = 8 Gf : 2 4 4 2 2 8 6 10 10 3 9 5 2 8 s t 8 4

Ford-Fulkerson Algorithm G: 10 10 s 0 6 X 10 2 0 4 2 2 8 8 3 2 8 X 9 4 6 X 0 6 5 0 6 X 10 10 10 t 16 Flow value = 10 Gf : s 2 4 4 10 2 8 6 10 10 3 7 5 10 t 2 5

Ford-Fulkerson Algorithm 2 G: 10 10 s 6 8 X 10 2 X 2 0 3 0 2 X 4 8 8 8 9 4 66 6 8 X 10 5 10 10 t 18 Flow value = 16 2 Gf : 4 4 6 s 10 2 8 6 4 4 3 1 5 10 6 t 8 6

Ford-Fulkerson Algorithm G: 10 10 s 8 9 X 10 2 2 3 X 4 2 0 8 7 X 8 3 8 9 X 9 4 66 8 9 X 10 5 10 10 t 19 Flow value = 18 2 2 Gf : 2 4 8 s 10 2 8 6 2 2 3 1 5 10 8 t 8 7

Ford-Fulkerson Algorithm G: 10 10 s 9 10 2 3 4 2 0 7 8 3 9 9 4 66 9 10 5 10 10 t Flow value = 19 3 2 Gf : s 1 10 2 7 1 3 9 4 1 9 6 1 5 10 t 9 8

Ford-Fulkerson Algorithm G: 10 10 s 9 10 2 3 4 2 0 7 8 3 9 9 4 66 9 10 5 10 10 Cut capacity = 19 t Flow value = 19 3 2 Gf : s 1 10 2 7 1 3 9 4 1 9 6 1 5 10 t 9 9