Separating bichromatic point sets by two disjoint isothetic rectangles

Given a set P of red points and a set Q of blue points in a plane with total size n, we investigate the problem of finding two disjoint isothetic rectangles containing all the points of Q, avoiding any points of P. Such rectangles are called two separating disjoint isothetic rectangles. We first compute two separating disjoint axis-aligned rectangles in O(n log n) time. Then, we relax the axis-aligned constraint and report all combinatorially different two separating disjoint isothetic rectangles. To compute these rectangles, we introduce some events by rotating the coordinate system and processing these events. Computing and processing all of the events are done in O(n(2) log n) time. Thus, our algorithm reports all combinatorially different separating rectangles in O(n(2) log n) time. (C) 2016 Sharif University of Technology. All rights reserved.