Breaking the O(n2.5) Deterministic Time Barrier for Undirected Unit-Capacity Maximum Flow

Abstract

This paper gives the first o(n2.5) deterministic algorithm for the maximum flow problem in any undirected unit-capacity graph with no parallel edges. In an n-vertex, m-edge graph with maximum flow value v, our running time is O(n9/4v1/8) = O(n2.375). Note that v ≤ n for simple unit-capacity graphs. The previous deterministic algorithms [Karger and Levine 1998] achieve O(m+nv3/2) and O(nm2/3v1/6) time bound, which are both O(n2.5) for dense simple graphs and v = Θ(n).