  The $k$-center problem is a classical combinatorial optimization problem
which asks to find $k$ centers such that the maximum distance of any input
point in a set $P$ to its assigned center is minimized. The problem allows for
elegant $2$-approximations. However, the situation becomes significantly more
difficult when constraints are added to the problem. We raise the question
whether general methods can be derived to turn an approximation algorithm for a
clustering problem with some constraints into an approximation algorithm that
respects one constraint more. Our constraint of choice is privacy: Here, we are
asked to only open a center when at least $\ell$ clients will be assigned to
it. We show how to combine privacy with several other constraints.
