I am searching for the name of / literature to the algorithmic problem as follows:Given a metric space $(M,d)$, a finite Subset $X = \{ x_1, \dots, x_n \} \subset M$ and a fixed Radius $R > 0$, find the maximum amount of points being enclosed by a ball of radius $R$. Alternatively, find $N$, such that  $ N = \max_{x \in M} |X \cap B_R(x)| $I only know of the 1-center problem so far. But this tries to solve the problem for minimizing the radius of a ball containing all points within a set. I also found one paper discussing a $\mathcal{O}(|X|^2)$ solution for the euclidean plane. There it has been called Maximum-Enclosing-Disk-Problem. Any information regarding generalizations for $\mathbb{R}^D, D > 2$ or different metrics, would be helpful. I am not very experienced with computational geometry and the theory of algorithms, but I need to find current literature on this problem. Having a name, or a similar problem, on which this problem can be reduced, would be help me a lot. Also, if you know literature or keywords regarding approximation attempts.Thank you for your answers.Edit: As discussed in the comments, an arbitrary metric space might not even computable. However, as I didn't want to restrict the solution on real euclidean spaces (e.g. the space of strings provided with the edit-distance should be an option), I decided for the very general formulation of the problem.  
Find the maximum subset contained by a ball of radius R
ds.algorithms;optimization;computational geometry