1. Edmonds-Karp Algorithm
Lecture 14
Edmonds-Karp Algorithm

2. Edmonds-Karp Algorithm
The augmenting path is a shortest path from s to t in the residual graph (here, we count the number of edges for the shortest path).

3. Ford-Fulkerson Max Flow4 2 5 1 3 1 1 2 2 s 4 t 3 2 1 3
This is the original network.

4. Ford-Fulkerson Max Flow4 2 5 1 3 1 1 2 2 s 4 t 3 2 1 3
Choose a shortest path from s to t.

5. Ford-Fulkerson Max Flow4 2 5 1 3 1 1 2 2 s 4 t 3 2 1 3
This is residual graph after the 1st augmentation.

6. Ford-Fulkerson Max Flow4 2 5 1 3 1 1 2 2 s 4 t 3 2 1 3
Choose a shortest path from s to t.

7. Ford-Fulkerson Max Flow4 2 5 1 3 1 1 2 2 s 4 t 1 1 2 2 3
The residual graph after the 2nd augmentation.

8. Ford-Fulkerson Max Flow4 2 5 1 3 1 1 2 2 s 4 t 1 1 2 2 3
Choose a shortest path from s to t.

9. Ford-Fulkerson Max Flow3 2 5 1 1 2 1 1 1 2 2 s 4 t 1 1 2 2 3
The residual graph after the 3rd augmentation.

10. Lemma
Proof

12. Lemma
Proof

13. Theorem
Proof

18. Matching in Bipartite Graph
Maximum Matching

20. 1 1

21. Note: Every edge has capacity 1.

30. 1. Can we do augmentation directly
in bipartite graph?
2. Can we do those augmentation
in the same time?