Given a set $S$ of $n$ points in $\mathbb{R}^d$, where each point is associated with a binary label in $\{-1,1\}$. Set $S$ is known but the labelling assignment of its points is initially unknown. In a sequential fashion, at each time step, we can select one point of $S$ and ask for its label.

Question: What is the minimum number $q$ (expressed as a function of $n$ and $d$), over all possible sets $S\in\mathbb{R}^d$, of queries necessary to determine the labels of all points in $S$?

Example: If $d=1$ we clearly have that $q$ is logarithimic in $n$.