1. 7. Preflow-Push Demo

2. Preflow-Push Algorithm10 10 2 3 1 2 t s
Gf: 5 10 10 2 3 1 2 t 5

3. Preflow-Push Algorithm
10/10
10/10 2 3 1 2 t s
e=10
e=10
Gf: 5 10 10 2 3 1 2 t 5

4. Preflow-Push Algorithm
10/10
10/10
2/2 3 1 2 t s
e=3
e=12
Gf:
5/5 10 10 2 3 1 2 t 5

5. Preflow-Push Algorithm
Few relabels 1
10/10 s
5/5 s
10/10
Gf: G:
2/2 10 3 10 2 t
e=12 2 3 1 2 t 5

6. Preflow-Push Algorithm
Ready for push 1
10/10 s
5/5 s
10/10
Gf: G:
2/2 10 3 10 2 t
e=12 2 3 1 2 t 5

7. Preflow-Push Algorithm
Push from 1 to source
Update residual graph. 1
7/10 s
5/5 s
10/10
Gf: G:
2/2 10 3 7 3 2 t
e=12 2 3 1 2 t 5

8. Preflow-Push Algorithm
Active node 2.
Can push… 1
7/10 s
5/5 s
10/10
Gf: G:
2/2 10 3 7 3 2 t
e=12 2 3 1 2 t 5

9. Preflow-Push Algorithm
Active node 2.
Can push…pushes… 1
7/10 s
5/5 s
10/10
Gf: G:
2/2 10
3/3 7 3 2 t
e=9 2 3 1 2 t 5

10. Preflow-Push Algorithm1
Active node 2.
No edges in redidual graph flowing down.
Hence ready for Lift/relabel.
7/10 s
5/5 s
10/10
Gf: G:
2/2 10
3/3 7 3 2 t
e=9 2 3 1 2 t 5

11. Preflow-Push Algorithm
10/10
e=9 2
2/2 1
7/10 s s
3/3
Gf: G: 10
5/5 7 3 t 2 3 1 2 t
Active node 2
Ready for push 5

12. Preflow-Push Algorithm
1/10 2
2/2 1
7/10 s s
3/3
Gf: G: 1
5/5 7 3 t 9 2 3 1 2 t
2 pushes to source
No more active nodes
Main loop of the algorithm terminates.
Max flow found. 5