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Lecture 14

Lecture 14. Edmonds-Karp Algorithm. 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). Ford-Fulkerson Max Flow. 4. 2. 5. 1. 3. 1. 1. 2. 2. s. 4. t. 3. 2. 1. 3.

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Lecture 14

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  1. 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 Flow 4 2 5 1 3 1 1 2 2 s 4 t 3 2 1 3 This is the original network, plus reversals of the arcs.

  4. Ford-Fulkerson Max Flow 4 2 5 1 3 1 1 2 2 s 4 t 3 2 1 3 This is the original network, plus reversals of the arcs.

  5. Ford-Fulkerson Max Flow 4 2 5 1 3 1 1 2 2 s 4 t 1 2 1 2 3 This is the original network, plus reversals of the arcs.

  6. Ford-Fulkerson Max Flow 3 2 5 1 2 1 1 2 2 s 4 t 1 2 1 2 3 This is the original network, plus reversals of the arcs.

  7. Lemma Proof

  8. Lemma Proof

  9. Theorem Proof

  10. Matching in Bipartite Graph Maximum Matching

  11. 1 1

  12. Note: Every edge has capacity 1.

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

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