Finding monochromatic l-shapes in bichromatic point sets

Given a set R of red points and a set B of blue points in the plane of total size n, we study the problem of determining all angles for which there exists an L-shape containing all points from B without containing any points from R. We propose an algorithm to solve the problem in O(n2 log n) time and O(n) storage. We also describe an output-sensitive algorithm that reports all angles in O(n5/3+ + k log k) time and O(n5/3+ ) storage, where k is the number of reported angular intervals.

• Type: Conference
• Year: 2010
• Where: CCCG
• Authors: Farnaz Sheikhi, Mark de Berg, Ali Mohades, Mansoor Davoodi Monfared
• Keywords: Blue Points, CCCG 2010, Computational Geometry, Red Points, Total Size