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On the complexity of some common geometric location problems. (English) Zbl 0534.68032
The p-center problem with respect to a metric $\rho$ (on the plane) consists in producing p points for a given set of n points to minimize the maximal distance (in the metric $\rho)$ from the given points to their respective nearest produced points. The similar p-median problem is to minimize the sum of the considered distances. The main result of the paper states that both, p-center and p-median problem, are NP-hard for two metrics $\rho =\ell\sp 2,\ell\sp 1$. It is also proved that the p- center problem is NP-hard even if approximating it within 15 % for $\rho =\ell\sp 2$ and correspondingly within 50 % for $\rho =\ell\sp 1$.
Reviewer: D.Yu.Grigorev

68Q25Analysis of algorithms and problem complexity
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