Generating pseudo-random permutations and maximum flow algorithms

We describe a simple construction of a family of permutations with a certain pseudo-random property. Such a family can be used to derandomize a recent randomized maximum-flow algorithm of Cheriyan and Hagerup for all relatively dense networks. Hence this supplies a deterministic maximum-flow algorithm that works, on a network with n vertices and m edges, in time O(nm) for all m=Ω(n5/3 log n) (and in time O(nm log n) for all other values of n and m). This improves the running time of the best known deterministic maximum-flow algorithm, due to Goldberg and Tarjan, whose running time is O(nm log(n2/m)). © 1990.