On cutting a few vertices from a graph Original Research Article

We consider the problem of finding in an undirected graph a minimum cut that separates exactly a given number k of vertices. For general k (i.e. k is part of the input and may depend on n) this problem is NP-hard. We present for this problem a randomized approximation algorithm, which is useful when k is relatively small. In particular, for k=O(log n) we obtain a polynomial time approximation scheme, and for k=Ω(log n) we obtain an approximation ratio O(k/log n).