Inverse $$k$$ k -centrum problem on trees with variable vertex weights

Kien Nguyen () and Lam Anh ()

Mathematical Methods of Operations Research, 2015, vol. 82, issue 1, 19-30

Abstract: This paper considers a generalization of the inverse 1-median problem, the inverse $$k$$ 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 $$k$$ k -centrum problem on trees is $$\textit{NP}$$ NP -hard. Particularly, the inverse 1-center problem, a special case of the mentioned problem with $$k=1$$ k = 1 , on a tree with $$n$$ n vertices can be solved in $$O(n^{2})$$ O ( n 2 ) time. Copyright Springer-Verlag Berlin Heidelberg 2015

Keywords: Inverse problem; Center problem; Ordered median function; $$k$$ k -centrum; Tree (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s00186-015-0502-4

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