Metric k-center

In graph theory, the metric k-center or metric facility location problem is a combinatorial optimization problem studied in theoretical computer science. Given n cities with specified distances, one wants to build k warehouses in different cities and minimize the maximum distance of a city to a warehouse. In graph theory this means finding a set of k vertices for which the largest distance of any point to its closest vertex in the k-set is minimum. The vertices must be in a metric space, or in other words a complete graph that satisfies the triangle inequality.

Let ${\displaystyle (X,d)}$ be a metric space where ${\displaystyle X}$ is a set and ${\displaystyle d}$ is a metric
A set ${\displaystyle \mathbf {V} \subseteq {\mathcal {X}}}$, is provided together with a parameter ${\displaystyle k}$. The goal is to find a subset ${\displaystyle {\mathcal {C}}\subseteq \mathbf {V} }$ with ${\displaystyle |{\mathcal {C}}|=k}$ such that the maximum distance of a point in ${\displaystyle \mathbf {V} }$ to the closest point in ${\displaystyle {\mathcal {C}}}$ is minimized. The problem can be formally defined as follows:
For a metric space (${\displaystyle {\mathcal {X}}}$,d),

...
Wikipedia