Algorithm Running Time

Running time of the algorithm is dominated by the execution of steps 3 and 4:

• Number of possible partitions of S₀ into m clusters is $m ^ {\vert S_0\vert} = m ^ {\log \log(n)} = \log ^ {c} (n)$;
• For each partition we perform $O(\log(n) \log\log(n))$ operations in step 3.a and $O(n \log(n))$ operations in step 3.b, thus the overall running time of step 3 is $O(n \log^{c_1}(n))$;
• For each partition we perform O(n²) operations in step 4, thus the overall running time in step 4 is $O(n^2 \log ^ {c} (n)$;
• The overall running time of the algorithm is $O(n^2 \log ^ {c} (n))$;