An Inverse Branchweight Centroid Problem on Some Graphs

Given a graph G with a positive weight for each vertex in G, the branchweight centroid problem on G is to find a vertex in G with the minimum branchweight where the branchweight of a vertex means the maximum of the weights of its branches. In this paper we first introduce an inverse branchweight centroid problem on a tree T whose objective is to change the weights of the given tree T at minimum cost so that a specified vertex in T  becomes the branchweight centroid of T with respect to the new vertex weights. Then we give a mathematical formulation of this problem and suggest an efficient algorithm for it.