Abstract
This paper considers a generalization of the inverse 1-median problem, the inverse \(k\)-centrum problem, on trees with variable vertex weights. In contrast to the linear time solvability of the inverse 1-median problem on trees, we prove that the inverse \(k\)-centrum problem on trees is \(\textit{NP}\)-hard. Particularly, the inverse 1-center problem, a special case of the mentioned problem with \(k=1\), on a tree with \(n\) vertices can be solved in \(O(n^{2})\) time.
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The authors thank the referee for valuable suggestions. This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 101.01-2014.44.
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Nguyen, K.T., Anh, L.Q. Inverse \(k\)-centrum problem on trees with variable vertex weights. Math Meth Oper Res 82, 19–30 (2015). https://doi.org/10.1007/s00186-015-0502-4
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DOI: https://doi.org/10.1007/s00186-015-0502-4