Separating objects in the plane by wedges and strips Original Research Article

In this paper we study the separability of two disjoint sets of objects in the plane according to two criteria: wedge separability and strip separability. We give algorithms for computing all the separating wedges and strips, the wedges with the maximum and minimum angle, and the narrowest and the widest strip. The objects we consider are points, segments, polygons and circles. As applications, we improve the computation of all the largest circles separating two sets of line segments by a log n factor, and we generalize the algorithm for computing the minimum polygonal separator of two sets of points to two sets of line segments with the same running time.