Abstract

We show that the minimum cut problem for weighted undirected graphs can be solved in NC using three separate and independently interesting results. The first is an (m 2 =n)-processor NC algorithm for finding a (2 + ffl)-approximation to the minimum cut. The second is a randomized reduction from the minimum cut problem to the problem of obtaining a (2 + ffl)-approximation to the minimum cut. This reduction involves a natural combinatorial Set-Isolation Problem that can be solved easily in RNC. The third result is a derandomization of this RNC solution that requires a combination of two widely used tools: pairwise independence and random walks on expanders. We believe that the set-isolation approach will prove useful in other derandomization problems. The techniques extend to two related problems: we describe NC algorithms finding minimum k-way cuts for any constant k and finding all cuts of value within any constant factor of the minimum. Another application of these techni...

Citations