Separating bichromatic point sets by L-shapes

摘要

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(2)) time and O(n) storage, where n = vertical bar R vertical bar + vertical bar B vertical bar. We also describe an output-sensitive algorithm that reports these angles in O(n(8/5+epsilon) klogk) time and O(n(8/5+epsilon)) storage, where k is the number of reported angular intervals and epsilon > 0 is any fixed constant. (C) 2015 Elsevier B.V. All rights reserved.