15.082 & 6.855J & ESD.78J Algorithm Visualization The Ford-Fulkerson Augmenting Path Algorithm for the Maximum Flow Problem.

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& 6.855J & ESD.78J Algorithm Visualization The Ford-Fulkerson Augmenting Path Algorithm for the Maximum Flow Problem

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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