The Ford-Fulkerson Augmenting Path Algorithm for the Maximum Flow Problem Thanks to Jim Orlin & MIT OCW.

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Presentation transcript:

The Ford-Fulkerson Augmenting Path Algorithm for the Maximum Flow Problem Thanks to Jim Orlin & MIT OCW

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

3 Ford-Fulkerson Max Flow s t This is the original network, and the original residual network.

Ford-Fulkerson Max Flow Find any s-t path in G(x) s t

Ford-Fulkerson Max Flow Determine the capacity  of the path. Send  units of flow in the path. Update residual capacities s t

Ford-Fulkerson Max Flow Find any s-t path s t

Ford-Fulkerson Max Flow s t Determine the capacity  of the path. Send  units of flow in the path. Update residual capacities.

Ford-Fulkerson Max Flow s t Find any s-t path

Ford-Fulkerson Max Flow s t Determine the capacity  of the path. Send  units of flow in the path. Update residual capacities.

Ford-Fulkerson Max Flow s t Find any s-t path

Ford-Fulkerson Max Flow s t Determine the capacity  of the path. Send  units of flow in the path. Update residual capacities. 2

Ford-Fulkerson Max Flow s t Find any s-t path 2

Ford-Fulkerson Max Flow 2 1 s t 2 Determine the capacity  of the path. Send  units of flow in the path. Update residual capacities.

Ford-Fulkerson Max Flow 2 1 s t 2 There is no s-t path in the residual network. This flow is optimal

Ford-Fulkerson Max Flow 2 1 s t 2 These are the nodes that are reachable from node s. s

16 Ford-Fulkerson Max Flow s t Here is the optimal flow