Polylogarithmic time

Polylogarithmic time

An algorithm is said to run in polylogarithmic time if its time ${\displaystyle T(n)}$ is ${\displaystyle O{\bigl (}(\log n)^{k}{\bigr )}}$ for some constant ${\displaystyle k}$. Another way to write this is ${\displaystyle O(\log ^{k}n)}$.