On computing minimum (s, t)-cuts in digraphs

Let D=(V,E) be a simple digraph with n vertices and m edges, and s and t be vertices designated as a source and a sink. The currently fastest algorithm that computes a minimum (s,t)-cut in D runs in O(min{@n,n^2^/^3,m^1^/^2}m) time, where @n is the size of a minimum (s,t)-cut. In this paper, we define the non-eulerianness @m as the sum of |#incoming edges at u-#outgoing edges at u| over all [email protected]?V-{s,t}, and prove that a minimum (s,t)-cut in D can be obtained in O(min{[email protected](@[email protected])^1^/^2n,(@[email protected])^1^/^6nm^2^/^3}) time. This outperforms the previous algorithm when D is a dense digraph with small @m.