Abstract
The inverse p-median problem with variable edge lengths on graphs is to modify the edge lengths at minimum total cost with respect to given modification bounds such that a prespecified set of p vertices becomes a p-median with respect to the new edge lengths. The problem is shown to be strongly \({\mathcal{NP}}\)-hard on general graphs and weakly \({\mathcal{NP}}\)-hard on series-parallel graphs. Therefore, the special case on a tree is considered: It is shown that the inverse 2-median problem with variable edge lengths on trees is solvable in polynomial time. For the special case of a star graph we suggest a linear time algorithm.
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Baroughi Bonab, F., Burkard, R.E. & Gassner, E. Inverse p-median problems with variable edge lengths. Math Meth Oper Res 73, 263–280 (2011). https://doi.org/10.1007/s00186-011-0346-5
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DOI: https://doi.org/10.1007/s00186-011-0346-5