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  "body": "\n## Summary\n\nIn graph theory, the **metric $k$-center** problem or **vertex k-center problem** is a classical combinatorial optimization problem studied in theoretical computer science that is NP-hard. 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|063W5JMY85]], providing a [[complete graph|03WKB2H474]] that satisfies the [[triangle inequality|03HF5PMY5T]]. It has application in facility location and clustering.\n",
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