Weighted Euclidean Steiner Trees for Disaster-Aware Network Design

We consider the problem of constructing a Euclidean Steiner tree in a setting where the plane has been divided into polygonal regions, each with an associated weight. Given a set of points (terminals), the task is to construct a shortest interconnection of the points, where the cost of a line segment in a region is the Euclidean distance multiplied by the weight of the region. The problem is a natural generalization of the obstacle-avoiding Euclidean Steiner tree problem, and has obvious applications in network design. We propose an efficient heuristic strategy for the problem, and evaluate its performance on both randomly generated and near-realistic problem instances. The minimum cost Euclidean Steiner tree can be seen as an optical backbone network (a Spine) avoiding disaster prone areas, here represented as higher cost regions.