Maximum Flow
linear
programming
maximum
flow
v
s
source
t
w
destination /
sink
v
s
t
w
v
s
t
w
v
s
t
w
3
s
2
2
v
5
2
t
1
3
w
2
3
s
2
2
v
5
2
t
1
3
w
v
2
s
2
5
2
w
t
3
3
s
2
2
v
5
2
t
1
3
w
v
2
s
2
5
2
w
t
3
3
s
2
2
v
5
2
t
1
3
w
v
2
s
5
2
w
t
3
3
s
2
2
v
5
2
t
1
3
w
v
2
Except for s and t,
in-flow=out-flow
s
5 (1)
w
t
Greedy Algorithm
v
s
5
2
w
t
3
v
s
5
2
w
t
3
improvement: 3
flow units
v
s
5 (3)
w
t
3 (3)
v
s
5 (3)
w
t
v
s
5 (3)
w
t
3 (3)
v
s
5 (3)
w
t
3 (3)
v
improvement: 2
flow units
s
5 (3)
w
t
3 (3)
v
s
5 (3)
w
t
3 (3)
v
improvement: 2
flow units
s
5 (3)
w
t
3 (3)
v
s
5 (3)
w
t
3 (3)
v
improvement: 2
flow units
s
5 (3)
w
t
3 (3)
v
s
5 (3)
w
t
3 (3)
v
improvement: 2
flow units
s
5 (1)
w
t
3 (3)
3
s
2
2
v
5
2
t
1
3
w
v
2
s
5 (1)
w
t
Residual Flow Network
s
G
Gf
v
v
5 (3)
w
t
s
t
3 (3)
w
Residual Flow Network
s
G
Gf
v
v
5 (3)
w
t
s
3
2
3 (3)
w
t
Residual Flow Network
s
G
Gf
v
v
5 (3)
w
t
s
3
2
3 (3)
w
t
Residual Flow Network
G
Gf
v
s
v
3
0
5 (3)
w
t
s
3
2
3 (3)
w
t
Residual Flow Network
G
Gf
v
s
3
0
5 (3)
w
t
3 (3)
s
v
2
3
0 2
2
0
w
t
3
0
Residual Flow Network
G
Gf
v
s
v
3
5 (3)
w
t
3 (3)
2
s
3
2
2
w
3
t
Residual Flow Network
G
Gf
v
s
v
3
5 (3)
w
t
3 (3)
2
s
3
2
2
w
improvement: 2
flow units
3
t
Residual Flow Network
G
Gf
v
s
v
3
5 (3)
w
t
3 (3)
2
s
3
2
2
w
improvement: 2
flow units
3
t
Residual Flow Network
G
Gf
v
s
v
3
5 (1)
w
t
3 (3)
2
s
3
2
2
w
improvement: 2
flow units
3
t
Residual Flow Network
v
s
3
0
5 (1)
w
t
3 (3)
s
v
0
1
2 4
0
2
w
t
3
0
Residual Flow Network
v
s
3
5 (1)
w
t
s
v
2
1
2 4
3 (3)
w
3
t