Network flow and generalized path compression

An O(EVlog<supscrpt>2</supscrpt>V) algorithm for finding the maximal flow in networks is described. It is asymptotically better than the other known algorithms if E &equil; O(V<supscrpt>2−ε</supscrpt>) for some ε>0. The analysis of the running time exploits the discovery of a phenomenon similar to (but more general than) path compression, although the union find algorithm is not used. The time bound is shown to be tight in terms of V and E by exhibiting a family of networks that require Ω(EVlog<supscrpt>2</supscrpt>V) time.<supscrpt>++</supscrpt>