1. 7. Preflow-Push Demo

2. 2 Preflow-Push Algorithm s 2 1 t 10 2 G: 5 3 s 2 1 t 10 2 5 3 G f :

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

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

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

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

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

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

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

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

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

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