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Correctness of Edmonds-Karp

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Presentation on theme: "Correctness of Edmonds-Karp"— Presentation transcript:

1 Correctness of Edmonds-Karp
An edge serves as bottleneck at most n/2 times

2 An edge serves as bottleneck
Step k: Step k’’:

3 Bottleneck edge Step k: Step k+1 Step k’’:

4 Bottleneck edge Step k: Step k+1 Step k’ Step k’’:

5 The level number never decreases

6 The k-th iteration Residual graph BFS tree: the edges in red Level 3
2 4 4 4 4 6 8 6 2 6 s 1 3 9 5 1 t 9 9 BFS tree: the edges in red Level 3 2 4 4 4 4 6 8 6 2 6 s 1 3 9 5 1 t 9 9 Level 0 Level 1 Level 2

7 The (k+1)-th iteration Residual graph BFS tree: the edges in red
2 4 4 5 4 1 5 6 2 6 7 s 1 3 9 5 t 9 10 BFS tree: the edges in red Level 3 2 4 4 5 4 1 5 6 2 6 7 s 1 3 9 5 t 9 9 Level 0 Level 1 Level 2 Level 4

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