Abstract. Minimum cuts have been closely related to shortest paths in planar graphs via planar duality -so long as the graphs are undirected. Even maximum flows are closely related to shortest paths for the same reason -so long as the source and the sink are on a common face. In this paper, we give a correspondence between maximum flows and shortest paths via duality in directed planar graphs with no constraints on the source and sink. We believe this a promising avenue for developing algorithms that are more practical than the current asymptotically best algorithms for maximum st-flow.
Borradaile and Harutyunyan REF explored this path-flow duality further and showed a correspondence between maximum flows and shortest paths in directed planar graphs with no restriction on the locations of the source and the sink.
Maximum st-flow in directed planar graphs via shortest paths
ArXiv
ArXiv
Mathematics Computer Science