Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5775819 | Applied Mathematics and Computation | 2017 | 15 Pages |
Abstract
Given a set S of n line segments in the plane, we say that a region RâR2 is a stabber for S if R contains exactly one endpoint of each segment of S. In this paper we provide optimal or near-optimal algorithms for reporting all combinatorially different stabbers for several shapes of stabbers. Specifically, we consider the case in which the stabber can be described as the intersection of axis-parallel halfplanes (thus the stabbers are halfplanes, strips, quadrants, 3-sided rectangles, or rectangles). The running times are O(n) (for the halfplane case), O(nlogân) (for strips, quadrants, and 3-sided rectangles), and O(n2logân) (for rectangles).
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Mercè Claverol, Delia Garijo, Matias Korman, Carlos Seara, Rodrigo I. Silveira,