If unlabeled vertex j is connected to the front vertex i of the traversal queueby a directed edge from i to j with positive unused capacity rij= uij− xij , thenvertex j is labeled with lj, i+, where lj= min{li, rij}.If unlabeled vertex j is connected to the front vertex i of the traversal queueby a directed edge from j to i with positive flow xji, then vertex j is labeled withlj, i−, where lj= min{li, xji}.If this labeling-enhanced traversal ends up labeling the sink, the currentflow can be augmented by the amount indicated by the sink’s first label. Theaugmentation is performed along the augmenting path traced by following thevertex second labels from sink to source: the current flow quantities are increasedon the forward edges and decreased on the backward edges of this path. If, on theother hand, the sink remains unlabeled after the traversal queue becomes empty,the algorithm returns the current flow as maximum and stops.
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