An 0(EViog2V) algorithm for finding the maximal flow in networks is described. It is asymptotically better than the other known algorithms if E = O(V 2-~) for some e>0. The analysis of the running time exploits the discovery of a phenomenon similar to (but more general thanl path com~ pression, 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 ~(_EViog2V) ++ time.
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