26_2 - Chapter 26 Contents Contents. Maximum flow problem....

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1 Chapter 26 Maximum Flow How do we transport the maximum amount data from source to sink? Some of these slides are adapted from Lecture Notes of Kevin Wayne. Contents ± Contents. ± Maximum flow problem. ± Minimum cut problem. ± Max-flow min-cut theorem. ± Augmenting path algorithm. ± Capacity-scaling. ± Shortest augmenting path. ± An s-t cut is a node partition (S, T) s.t. s S, t T. ± The capacity of an s-t cut (S, T) is: ± Min s-t cut : find an s-t cut of minimum capacity. Cuts V v u T v S u v u c , , ). , ( s 2 3 4 5 6 7 t 15 5 30 15 10 8 15 9 6 10 10 10 15 4 4 Capacity = 30 Cuts ± An s-t cut is a node partition (S, T) s.t. s S, t T. ± The capacity of an s-t cut (S, T) is: ± Min s-t cut: find an s-t cut of minimum capacity. s 2 3 4 5 6 7 t 15 5 30 15 10 8 15 9 6 10 10 10 15 4 4 Capacity = 62 V v u T v S u v u c , , ). , ( Cuts ± An s-t cut is a node partition (S, T) s.t. s S, t T. ± The capacity of an s-t cut (S, T) is: ± Min s-t cut: find an s-t cut of minimum capacity. V v u T v S u v u c , , ). , ( s 2 3 4 5 6 7 t 15 5 30 15 10 8 15 9 6 10 10 10 15 4 4 Capacity = 28 Recall the example s 2 3 4 5 6 7 t 15 5 30 15 10 8 15 9 6 10 10 10 15 4
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26_2 - Chapter 26 Contents Contents. Maximum flow problem....

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