Repeatedly perform flow-improving operations until no further improvement is possible. Determine the smallest such unused capacity along the path. Once we have done this once for all possible directed paths, we can make no further improvements this way. A second way to make improvements is to consider arbitrary paths in which we allow some edges to be followed the wrong way. We can make an improvement along such a path if a.
All forward edges have unused capacity.
C. Practical Considerations 1. However, if we considered paths in the order ABC ADC we would get there in just two steps. To arrive at maximum flow most quickly, it turns out that we should consider the paths in the order they would be generated by a BFS starting at the source.