Separating Two Points with Obstacles in the Plane: Improved Upper and Lower Bounds

Given two points in the plane, and a set of "obstacles" given as curves through the plane with assigned weights, we consider the point-separation problem, which asks for the minimum-weight subset of the obstacles separating the two points. A few computational models for this problem have been previously studied. We give a unified approach to this problem in all models via a reduction to a particular shortest-path problem, and obtain improved running times in essentially all cases. In addition, we also give fine-grained lower bounds for many cases.