Abstract
The k-center problem is a well-known facility location problem and can be described as follows: Given a complete undirected graph G=(V,E), a metric d:V×V→ℝ + and a positive integer k, we seek a subset U ⊆ V of at most k centers which minimizes the maximum distances from points in V to U. Formally, the objective function is given by:
As a typical example, we may want to set up k service centers (e.g., police stations, fire stations, hospitals, polling centers) and minimize the maximum distances between each client and these centers. The problem is known to be \(\mathcal{NP}\)-hard [2].
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Lim, A., Rodrigues, B., Wang, F., Xu, Z. (2004). k-Center Problems with Minimum Coverage. In: Chwa, KY., Munro, J.I.J. (eds) Computing and Combinatorics. COCOON 2004. Lecture Notes in Computer Science, vol 3106. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27798-9_38
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DOI: https://doi.org/10.1007/978-3-540-27798-9_38
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