Embed Size (px)
Citation preview
Algorithm Visualization
The Ford-Fulkerson Augmenting Path Algorithm for the Maximum
Flow Problem
4
112
21
2
3
3
1
s
2
4
5
3
t
3
Ford-Fulkerson Max Flow
This is the original network, and the original residual network.
4
11
2
21
2
3
3
1
s
2
4
5
3
t
4
112
21
2
3
3
1
s
2
4
5
3
t
4
4
11
2
21
2
3
3
1
Ford-Fulkerson Max Flow
Find any s-t path in G(x)
s
2
4
5
3
t
4
112
21
2
3
3
1
s
2
4
5
3
t
5
4
1
1
2
13
Ford-Fulkerson Max Flow
Determine the capacity Δ of the path.
Send Δ units of flow in the path.Update residual capacities.
11
1
21
2
3
2
1
s
2
4
5
3
t
4
112
21
2
3
3
1
s
2
4
5
3
t
6
4
1
1
2
13
Ford-Fulkerson Max Flow
Find any s-t path
11
1
21
2
3
2
1
s
2
4
5
3
t
4
112
21
2
3
3
1
s
2
4
5
3
t
7
4
2
1
1
1
12
2
1
1
1
13
Ford-Fulkerson Max Flow
11
1
1
3
2
1
s
2
4
5
3
t
Determine the capacity Δ of the path.
Send Δ units of flow in the path.Update residual capacities.
4
112
21
2
3
3
1
s
2
4
5
3
t
8
4
2
1
1
1
12
2
1
1
1
13
Ford-Fulkerson Max Flow
11
1
1
3
2
1
s
2
4
5
3
t
Find any s-t path
4
112
21
2
3
3
1
s
2
4
5
3
t
9
11 1
11
4
1
2
1
12
11
3
Ford-Fulkerson Max Flow
113
2
1
s
2
4
5
3
t
Determine the capacity Δ of the path.
Send Δ units of flow in the path.Update residual capacities.
4
112
21
2
3
3
1
s
2
4
5
3
t
10
11 1
11
4
1
2
1
1
2
2
11
3
Ford-Fulkerson Max Flow
113
2
1
s
2
4
5
3
t
Find any s-t path
4
112
21
2
3
3
1
s
2
4
5
3
t
11
1
11
2 1 1
11
4
2
2
1
1
2
21
Ford-Fulkerson Max Flow
113
1
1
s
2
4
5
3
t
2
Determine the capacity Δ of the path.
Send Δ units of flow in the path.Update residual capacities.
4
112
21
2
3
3
1
s
2
4
5
3
t
12
11
2 1 1
11
4
2
2
1
1
2
21
Ford-Fulkerson Max Flow
113
1
1
s
2
4
5
3
t
2
Find any s-t path
4
112
21
2
3
3
1
s
2
4
5
3
t
13
111
11
4
13
11
2 1 1
3
2
21
21
Ford-Fulkerson Max Flow
2
1s
2
4
5
3
t
2
Determine the capacity Δ of the path.
Send Δ units of flow in the path.Update residual capacities.
4
112
21
2
3
3
1
s
2
4
5
3
t
14
111
11
4
13
11
2 1 1
3
2
21
21
Ford-Fulkerson Max Flow
2
1s
2
4
5
3
t
2
There is no s-t path in the residual network. This flow is optimal
4
112
21
2
3
3
1
s
2
4
5
3
t
15
111
11
4
13
11
2 1 1
3
2
21
21
Ford-Fulkerson Max Flow
2
1s
2
4
5
3
t
2
These are the nodes that are reachable from node s.
s
2
4
5
3
4
112
21
2
3
3
1
s
2
4
5
3
t
16
Ford-Fulkerson Max Flow
1
1
2
2
2
1
2s
2
4
5
3
t
Here is the optimal flow
MITOpenCourseWarehttp://ocw.mit.edu
15.082J / 6.855J / ESD.78J Network OptimizationFall 2010
For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.
![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://img.pdfslide.net/doc/110x75/5fc5c36ad951d42aad3d1c2d/cones-graphs-and-optimal-scalings-of-matrices-cones-graphs-and-matrices-123-eg.jpg)
