7. Edmonds-Karp Algorithm
Algorithm Design by Éva Tardos and Jon Kleinberg • Copyright © 2005 Addison Wesley • Slides by Kevin Wayne
Edmonds-Karp 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
Edmonds-Karp 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
Edmonds-Karp Algorithm
G:
10 X
8
10
0
10
s
2
0 2
X
4
2 0
8
8
3
0
9
4
60
0 2
X
10
5
8
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
G:
2
2
4
2 0
8
8
3
0 2
X
9
10
10
s
0 2
X
10
4
60
5
2
10
10 X
8
10
t
12
Flow value = 10
2
2
Gf:
2
4
2
10
s
10
2
8
6
8
3
9
5
2
t
8
5
G:
2
2
4
2 0
8
8
3
2 8
X
9
10
10
s
2 8
X
10
4
6X
0
6
5
2 8
X
10
10
10
t
18
Flow value = 12
2
2
Gf:
2
4
2
s
10
2
8
6
8
8
3
7
5
10
2
t
2
6
G:
2
2 3
X
4
2 0
8 7
X
8
3
8 9
X
9
10
10
s
8 9
X
10
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
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
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