The Ford-Fulkerson method is simple: start with zero flow, then repeatedly find augmenting paths and push flow through them until no path remains. Pseudocode:
Initialize all flows to .
While there exists an augmenting path in the residual graph:
- Find the bottleneck capacity.
- Push that much flow along the path.
- Update the residual graph. The method guarantees you find the maximum flow. The question is: how do you find augmenting paths?