A New Approximation Algorithm for the Unbalanced Min s-t Cut Problem

Let k be an input parameter. An s-t cut is of k-size if its s-side has size at most k. The Min k-Size s-t Cut problem asks to find a k-size s-t cut with the minimum capacity. Being the unbalanced version of the famous Min s-t Cut problem, this problem is fundamental and has extensive applications, especially in community identification in social and information networks. In this paper, we give a new k+1/k+1-k*-approximation algorithm for the Min k-Size s-t Cut problem, where k* is the size of s-side of an optimal solution.