k-Center Problems with Minimum Coverage
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,...
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| Main Authors: | , , , |
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| Format: | text |
| Language: | English |
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Institutional Knowledge at Singapore Management University
2004
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| Subjects: | |
| Online Access: | https://ink.library.smu.edu.sg/lkcsb_research/2400 https://doi.org/10.1007/978-3-540-27798-9_38 |
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| Institution: | Singapore Management University |
| Language: | English |
| Summary: | 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: min U⊆V,|U|≤k max v∈V min r∈Ud(v,r).
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 NP-hard [2]. |
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