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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?

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    $\begingroup$ Sure, iterate over each subset of $ k $ vertices, return the one with the smallest maximum distance to the subset. If you want an efficient algorithm, the problem is NP-hard in 2 or more dimensions. $\endgroup$ Commented Oct 6, 2017 at 20:32

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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.

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