ford fulkerson algo
10
Algorithm Design by Éva Tardos and Jon Kleinberg • Copyright © 2005 Addison Wesley • Slides by Kevin Wayne 7. Ford-Fulkerson Demo
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Transcript of ford fulkerson algo
Algorithm Design by Éva Tardos and Jon Kleinberg • Copyright © 2005 Addison Wesley • Slides by Kevin Wayne
7. Ford-Fulkerson Demo
2
Ford-Fulkerson Algorithm
s
2
3
4
5 t 10
10
9
8
4
10
10 6 20
0
0
0 0 0
00
G:
Flow value = 0
0
flowcapacity
3
Ford-Fulkerson Algorithm
s
2
3
4
5 t 10
10
9
8
4
10
10 6 20
0
0
0 0 0
00
G:
s
2
3
4
5 t 10 9
4
10 6 2 Gf:
10 8
10
8 8
8
X X
X
0
Flow value = 0
capacity
residual capacity
flow
4
Ford-Fulkerson Algorithm
s
2
3
4
5 t 10
10
9
8
4
10
10 6 28
0
0
0 0 8
80 0
G:
s
2
3
4
5 t 10
4
10 6 Gf:
8
8 8
9
22
2
10
210
XX
X2X
Flow value = 8
5
0
Ford-Fulkerson Algorithm
s
2
3
4
5 t 10
10
9
8
4
10
10 6 210
0
0
0 2 10
82
G:
s
2
3
4
5 t
4
2 Gf:
10
810
2 10 7
10 6
X
66
6
X
X
8X
Flow value = 10
6
Ford-Fulkerson Algorithm
s
2
3
4
5 t 10
10
9
8
4
10
10 6 210
0
6
6 8 10
82
G:
s
2
3
4
5 t1
6 Gf:
10
8 10
8
6
6
6
4
4
4
2
X
8
2
8
X
X
0X
Flow value = 16
7
Ford-Fulkerson Algorithm
s
2
3
4
5 t 10
10
9
8
4
10
10 6 210
2
8
8 8 10
80
G:
s
2
3
4
5 t
6 2 Gf:
10
10
8
6
8
8
2
2 1
2
8 2
X
9
7 9
X
X
9X
X 3
Flow value = 18
8
Ford-Fulkerson Algorithm
s
2
3
4
5 t 10
10
9
8
4
10
10 6 210
3
9
9 9 10
70
G:
s
2
3
4
5 t 1 9
1
1 6 2 Gf:
10
7 10
6
9
9
3
1
Flow value = 19
9
Ford-Fulkerson Algorithm
s
2
3
4
5 t 10
10
9
8
4
10
10 6 210
3
9
9 9 10
70
G:
s
2
3
4
5 t 1 9
1
1 6 2 Gf:
10
7 10
6
9
9
3
1
Flow value = 19Cut capacity = 19
9
Ford-Fulkerson Algorithm
s
2
3
4
5 t 10
10
9
8
4
10
10 6 210
3
9
9 9 10
70
G:
s
2
3
4
5 t 1 9
1
1 6 2 Gf:
10
7 10
6
9
9
3
1
Flow value = 19Cut capacity = 19
![Cones, Graphs and Optimal Scalings of MatricesCONES, GRAPHS AND MATRICES 123 e.g. Ford-Fulkerson [14, Ch. III], see in particular the out-of-kilter algorithm found there and in Fulkerson](https://static.fdocuments.us/doc/165x107/5fc5c36ad951d42aad3d1c2d/cones-graphs-and-optimal-scalings-of-matrices-cones-graphs-and-matrices-123-eg.jpg)
