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DAA | Ford Fulkerson Algorithm

DAA | Ford Fulkerson Algorithm with daa tutorial, introduction, Algorithm, Asymptotic Analysis, Control Structure, Recurrence, Master Method, Recursion Tree Method, Sorting Algorithm, Bubble Sort, Selection Sort, Insertion Sort, Binary Search, Merge Sort, Counting Sort, etc.

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Ford-Fulkerson Algorithm

Initially, 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.

Ford-Fulkerson Algorithm

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.

Ford-Fulkerson Algorithm
Ford-Fulkerson Algorithm
Next TopicMaximum bipartite matching




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