FordFulkerson AlgorithmInitially, the flow of value is 0. Find some augmenting Path p and increase flow f on each edge of p by residual Capacity c_{f} (p). When no augmenting path exists, flow f is a maximum flow. FORDFULKERSON 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 FORDFULKERSON (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 G_{f}. 5. do c_{f} (p)←min?{ C_{f} (u,v):(u,v)is on p} 6. for each edge (u, v) in p 7. do f [u, v] ← f [u, v] + c_{f} (p) 8. f [u, v] ←f[u,v] Example: Each Directed Edge is labeled with capacity. Use the FordFulkerson algorithm to find the maximum flow. Solution: The left side of each part shows the residual network G_{f} with a shaded augmenting path p,and the right side of each part shows the net flow f.
Next TopicMaximum bipartite matching
