Is there any algorithm with time complexity O(lg * n) (iterated logarithm function)?

Question

In computer science, the iterated logarithm of n, written log* n (usually read "log star"), is the number of times the logarithm function must be iteratively applied before the result is less than or equal to 1. The simplest formal definition is the result of this recursive function:

Is there any algorithm with time complexity O(lg * n) ?

Answer 1

If you implement union find algorithm with path compression and union by rank, both union and find will have complexity O(log*(n)).