Summary: Generating Pseudo-Random Permutations and Maximum Flow
IBM Almaden Research Center, 650 Harry Road, San Jose, CA 95120 ,USA
and Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, ISRAEL
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 al-
gorithm of Cheriyan and Hagerup for all relatively dense networks. Hence this supplies a de-
terministic maximum-flow algorithm that works, on a network with n vertices and m edges, in
time O(nm) for all m = (n5/3
log n) (and in time O(nmlogn) 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(nmlog(n2
Keywords: maximum-flow algorithms, design of algorithms, derandomization, pseudo-random
permutations, longest common ascending subsequence.
1 The main results
Two permutations = (1), . . . , (n) and = (1), . . . , (n) of 1, . . . , n have a common ascending