The metric k-center problem is a classic problem in computer science and operations research, particularly in the field of combinatorial optimization and facility location. The problem can be described as follows: Given a metric space (a set of points with a distance function that satisfies the properties of a metric) and a positive integer \( k \), the goal is to choose \( k \) centers from a set of points such that the maximum distance from any point in the metric space to the nearest center is minimized.
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