Abstract

We describe an O(min(m; n 3=2 )m 1=2 )-time algorithm for finding maximum flows in undirected networks with unit capacities and no parallel edges. This improves upon the previous bound of Karzanov and Even and Tarjan when m = !(n 3=2 ), and upon a randomized bound of Karger when v = \Omega\Gamma n 7=4 =m 1=2 ). (Here v is the maximum flow value.) 1 Introduction In this paper we consider the undirected maximum flow problem in a network with unit capacities and no parallel edges. Until recently, the fastest known way to solve this problem was using a reduction to the directed problem with unit capacities and no parallel arcs. Karzanov [7] and Even and Tarjan [2] have shown that Dinitz's blocking flow algorithm [1], applied to the directed problem, runs in O(min(m 1=2 ; n 2=3 )m) time. (Here n and m is the number of input vertices and edges, respectively.) Recently, Karger [6] developed two randomized algorithms for the undirected problem, with running times of O (m 5...

Citations