Abstract
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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Notes
D.S. Hochbaum and D.B. Shmoys. A unified approach to approximation algorithms for bottleneck problems. Journal of the ACM, 33: 533–550, 1986.
W.L. Hsu and G.L. Nemhauser. Easy and hard bottleneck location problems. Discrete Applied Mathematics, 1: 209–216, 1979.
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© 2003 Springer-Verlag Berlin Heidelberg
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Vazirani, V.V. (2003). k-Center. In: Approximation Algorithms. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04565-7_5
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DOI: https://doi.org/10.1007/978-3-662-04565-7_5
Publisher Name: Springer, Berlin, Heidelberg
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