The k-centrum multi-faculty location problem
Discrete Applied Mathematics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The Complexity Analysis of the Inverse Center Location Problem
Journal of Global Optimization
The inverse 1-median problem on a cycle
Discrete Optimization
Discrete Optimization
Algorithmic results for ordered median problems
Operations Research Letters
Discrete Applied Mathematics
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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.