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Ford-Fulkerson AlgorithmInitially, the flow of value is 0. Find some augmenting Path p and increase flow f on each edge of p by residual Capacity cf (p). When no augmenting path exists, flow f is a maximum flow. FORD-FULKERSON METHOD (G, s, t) 1. Initialize flow f to 0 2. while there exists an augmenting path p 3. do argument flow f along p 4. Return f
FORD-FULKERSON (G, s, t)
1. for each edge (u, v) ∈ E [G]
2. do f [u, v] ← 0
3. f [u, v] ← 0
4. while there exists a path p from s to t in the residual network Gf.
5. do cf (p)←min?{ Cf (u,v):(u,v)is on p}
6. for each edge (u, v) in p
7. do f [u, v] ← f [u, v] + cf (p)
8. f [u, v] ←-f[u,v]
Example: Each Directed Edge is labeled with capacity. Use the Ford-Fulkerson algorithm to find the maximum flow. 
Solution: The left side of each part shows the residual network Gf with a shaded augmenting path p,and the right side of each part shows the net flow f.  
Next TopicMaximum bipartite matching
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