What is beta and k parameter in Incremental Decision Tree
It appears that $\beta$ is a constant, and $k$ ranges over the integers.  See paragraph 3 of Section IV.B.
Line 1 of Algorithm 2 tells you that $\beta$ is a parameter: it says &quot;Select parameters $\beta$ and ...&quot;  Based on the body text in Section IV.B, presumably &quot;if $t= \beta^k$&quot; means &quot;if there exists $k \in \mathbb{N}$ such that $t=\beta^k$&quot;.