Inverse multiobjective shortest path problem under the bottleneck type weighted Hamming distance

Given a network G = (V, A, c), a source node s and a set of directed paths ᴨ from s to all other nodes, an inverse multiobjective shortest path problem is to modify the cost matrix c as little as possible so that every path P in ᴨ becomes an efficient path. The modification can be measured by various distances. In this paper, we consider the bottleneck type weighted Hamming distance and propose an algorithm to solve the inverse multiobjective shortest path problem under the bottleneck type weighted Hamming distance when the network is an augmented tree.