Inverse obnoxious p-median location problems on trees with edge length modifications under different norms

Abstract

In this paper, we consider an inverse obnoxious p-median location problem with p≥2 on trees in which the aim is to change the edge lengths at the minimum total cost so that a predetermined set of p vertices becomes an obnoxious p-median location. A novel combinatorial algorithm with O(p2|V(T)|2log2⁡|V(T)|) time complexity is proposed for obtaining an optimal solution of the problem under the weighted Manhattan norm. Moreover, optimal solution algorithms with O(p2|V(T)|) time complexity are developed for the problem under the weighted Chebyshev norm and the weighted bottleneck-type Hamming distance.