Finding k Cuts within Twice the Optimal

Two simple approximation algorithms for the minimum $k$-cut problem are presented. Each algorithm finds a $k$ cut having weight within a factor of $(2-2/k)$ of the optimal. One of our algorithms is particularly efficient---it requires a total of only $n-1$ maximum flow computations for finding a set of near-optimal $k$ cuts, one for each value of $k$ between 2 and $n$.