- The Ford-Fulkerson method is iterative
- This method depends on three ideas:
- Augmenting paths
- Residual networks
- Simplified Pseudo-code:
initialize flow f to 0 while there exist an augmenting path p do augmented flow f along p return f
- An augmenting path is a simple path from source to sing in the residual network
- Each path have alternative free and matched edges in such way that begins and ends with free vertices.
- Definition: Each edge on an augmenting path admits some additional positive flow to without violating the capacity constrain on the edge.
- Minimum cut of a network: A cut whose capacity is minimum over all cuts on the network.
- Max-flow min-cut theorem: A flow is maximum if and only if its residual network contains no augmenting path.
Net-flow Across Cut (including net-flow between vertices):
Capacity (only edges going from source to sink ):
for each edge
do // :flow
while there exist a path from to in the residual network
do is in // : residual capacity
for each edge in
do // : path
Using either dept-first search or breadth-first search, the time to find a path in a residual network is
Total running time is where is the maximum flow found
Note: If you find any mistake please let me know