A O(nm log(U/n)) time maximum flow algorithm

In this paper, we present an O(nm log(U/n)) time maximum flow algorithm. If U = O(n) then this algorithm runs in O(nm) time for all values of m and n. This gives the best available running time to solve maximum flow problems satisfying U = O(n). Furthermore, for unit capacity networks the algorithm runs in O(n^2/3m) time. It is a two-phase capacity scaling algorithm that is easy to implement and does not use complex data structures.