Let T = (V, E) be a tree. A core of T is a path P, for which the sum of the weighted distances from all vertices to this path is minimized. In this paper, we consider the semi-obnoxious case in which the vertices have positive or negative weights. We prove that, when the sum of the weights of...

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 <InlineEquation ID="IEq1">...</inlineequation>