Sharif University of Technology Scientia Iranica 1026-3098 23 3 2016 06 01 Separating bichromatic point sets by two disjoint isothetic rectangles Separating bichromatic point sets by two disjoint isothetic rectangles 1228 1238 3891 10.24200/sci.2016.3891 EN Zahra Moslehi Amirkabir University of Tech. Alireza Bagheri Amirkabir University of Tech. Journal Article 2015 04 07 Given a set P of red points and a set Q of blue points in the plane of 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 first compute two separating disjoint axis-aligned rectangles in O(n log n) time. Then, we relax the axis-aligned constraint and report all combinatorially dierent two separating disjoint isothetic rectangles. To compute these rectangles, we introduce some events by rotating the coordinate system and process these events. Computing and processing all of the events are done in O(n^2 log n) time. Thus, our algorithm reports all combinatorially dierent separating rectangles in O(n^2 log n) time. https://scientiairanica.sharif.edu/article_3891_d675668fb71d478966c934e9add81ea2.pdf