Max-Flow on Regular Spaces

The max-flow and max-coflow problem on directed graphs is studied in the common generalization to regular spaces, i.e., to kernels or row spaces of totally unimodular matrices. Exhibiting a submodular structure of the family of paths within this model we generalize the Edmonds-Karp variant of the classical Ford-Fulkerson method and show that the number of augmentations is quadratically bounded if augmentations are chosen along shortest possible augmenting paths.