Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
414250 | Computational Geometry | 2015 | 15 Pages |
Abstract
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(n2)O(n2) time and O(n)O(n) storage, where n=|R|+|B|n=|R|+|B|. We also describe an output-sensitive algorithm that reports these angles in O(n8/5+ε+klogk)O(n8/5+ε+klogk) time and O(n8/5+ε)O(n8/5+ε) storage, where k is the number of reported angular intervals and ε>0ε>0 is any fixed constant.
Keywords
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Farnaz Sheikhi, Ali Mohades, Mark de Berg, Mansoor Davoodi,