Running Time

The algorithm runs in $O(N \times f(n,m))$, where N is the number of clusters and f(n,m) is the time to find the minimum cut in an unweighted, undirected graph with n vertices and m edges. The fastest min-cut algorithms known today (for undirected, unweighted graphs) are:

• Deterministic: O(mn) [14], [17]
• Randomized: O(mlog³n) [10]

The deterministic worst case running time for the algorithm is therefore O(mn²) (since the number of clusters is at most n). However, we usually expect N<<n.