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Table 1 Time complexity estimations of the steps of the random swap algorithm, and the observed numbers as the averages over the first 500 iterations for data set Bridge (N = 4096, k = 256, N/k = 16, α ≈ 8)

From: Efficiency of random swap clustering

Step Time complexity Observed number of steps at iteration
50 100 500
Prototype swap 2 2 2 2
Cluster removal 2N 7526 8448 10,137
Cluster addition 2N 8192 8192 8192
Prototype update 4N/k + 2α 53 61 60
K-means iterations ≤ 4αN 300,901 285,555 197,327
Total O(αN) 316,674 302,258 215,718