Given n points in the plane with nonnegative weights, the inverse Fermat-Weber problem consists in changing the weights at minimum cost such that a prespecified point in the plane becomes the Euclidean 1-median. The cost is proportional to the increase or decrease of the corresponding weight. In...

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>

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...

We study budget constrained network improvement and degrading problems based on the vertex 1-center problem on graphs: given a graph with vertex weights and edge lengths the task is to decrease and increase the vertex weights within certain limits such that the optimal 1-center objective value...

Let a connected undirected graph G  =  (V, E) be given. In the classical p-median problem we want to find a set X containing p points in G such that the sum of weighted distances from X to all vertices in V is minimized. We consider the semi-obnoxious case where every vertex has either a...

Let a connected undirected graph G  =  (V, E) be given. In the classical p-median problem we want to find a set X containing p points in G such that the sum of weighted distances from X to all vertices in V is minimized. We consider the semi-obnoxious case where every vertex has either a...