Analysis:

Depends on method for finding augmenting path.

Use breadth-first search (Edmonds-Karp Algorithm). Thus, the augmenting path is shortest from s to t.

Theorem 27.9

The total number of augmentations is O(VE), O(E) per augmentation. Thus the algorithm has run time O(VE²).

Preflow-Push method yields O(V²E) (Section 27.4), and
Lift-to-Front method yields O(V³) (Section 27.5).