Many algorithms and data structures have iterated logarithms ($\log^\star n$) in their runtimes. This function is the discrete inverse of tetration, in that
$$\log_a^\star (a \uparrow \uparrow b) = b$$
There’s another inverse to tetration called the superroot, which satisfies this definition:
$$\sqrt[b]{a \uparrow \uparrow b}_S = a$$
I’ve never encountered this function in any context in algorithms or data structures. While the iterated logarithm naturally arises when, well, iterating logarithms, I don’t have any intuition for what the superroot does or where it would arise.
Does this function actually get used in the analysis of any algorithms or data structures?
