Separating bichromatic point sets by L-shapes

Given a set R of red points and a set B of blue points in the plane, we study the problem of determining all angles for which there exists an L-shape containing all points from B and no points from R. We propose a worst-case optimal algorithm to solve this problem in O(n) time and O(n) storage, where n = |R| + |B|. We also describe an output-sensitive algorithm that reports these angles in O(n + k log k) time and O(n) storage, where k is the number of reported angular intervals and ε > 0 is any fixed constant.