I'm wondering if there is an algorithm that calculates the optimal solution of a typical k-center problem (more than one dimension). I've tried, but without success, to find this algorithm. Does such an algorithm exist?
An optimal solution for the k-center problem can be found by an exhaustive search over the solution space, and by picking the best solution. The problem is NP-Hard for more than 2 dimensions, and moreover any $\delta$-approximation for $\delta < 2$ is NP-hard.