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Article

Keywords:
$p$-median problem; $NP$-complete; communication networks; $m$-center problem
Summary:
It is shown that the problem of finding a minimum $k$-basis, the $n$-center problem, and the $p$-median problem are $NP$-complete even in the case of such communication networks as planar graphs with maximum degree 3. Moreover, a near optimal $m$-center problem is also $NP$-complete.
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