Consider the following application. Given a set of cities, with intercity distances specified, pick k cities for locating warehouses in so as to minimize the maximum distance of a city from its closest warehouse. We will study this problem, called the k-center problem, and its weighted version, under the restriction that the edge costs satisfy the triangle inequality. Without this restriction, the k-center problem cannot be approximated within factor α(n), for any computable function α(n), assuming P ≠ NP (see Exercise 5.1).
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