Optimal algorithms for inverse vertex obnoxious center location problems on graphs

In an inverse vertex obnoxious center location problem, the aim is to modify the edge lengths at minimum total cost with respect to the modification bounds such that a predetermined vertex becomes a vertex obnoxious center location under the new edge lengths. We develop a linear time combinatorial method for the problem with edge length augmentation. For the reduction case, an algorithm with cubic running time is devised. We also show that the problem with both edge length augmentation and reduction can be solved in sextic time.