Online Max-flow Learning via Augmenting and De-augmenting Path

This paper presents an augmenting path based online max-flow algorithm. The proposed algorithm handles graph changes in chunk manner, updating residual graph in response to edge capacity increase, decrease, edge/node adding and removal. All possible graph changes are abstracted into two key graph changes, which are capacity decrease and in- crease. For capacity decrease, we release the occupied capacity by cycle cancellation and path de-augmentation to enable the capacity decrease. For capacity increase, we augment all s-t paths newly formed to update the current max-flow model. The theoretical guarantee of our algorithm is that online max- flow is always equal to batch retraining. Experiments show the deterministic computational cost save (i.e., gain) of our algorithm w.r.t batch retraining in handling graph edge adding.