Abstract
The convex ordered median problem is a generalization of the median, the k-centrum or the center problem. The task of the associated inverse problem is to change edge lengths at minimum cost such that a given vertex becomes an optimal solution of the location problem, i.e., an ordered median. It is shown that the problem is NP-hard even if the underlying network is a tree and the ordered median problem is convex and either the vertex weights are all equal to 1 or the underlying problem is the k-centrum problem. For the special case of the inverse unit weight k-centrum problem a polynomial time algorithm is developed.
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This research has been supported by the Austrian Science Fund (FWF) Project P18918-N18.
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Gassner, E. An inverse approach to convex ordered median problems in trees. J Comb Optim 23, 261–273 (2012). https://doi.org/10.1007/s10878-010-9353-3
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DOI: https://doi.org/10.1007/s10878-010-9353-3