Introduction to VLSI Systems
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
An Optimal Worst Case Algorithm for Reporting Intersections of Rectangles
IEEE Transactions on Computers
Algorithms for Reporting and Counting Geometric Intersections
IEEE Transactions on Computers
Optimizing Pairwise Box Intersection Checking on GPUs for Large-Scale Simulations
ACM Transactions on Modeling and Computer Simulation (TOMACS)
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In this correspondence we reconsider three geometrical problems for which we develop divide-and-conquer algorithms. The first problem is to find all pairwise intersections among a set of horizontal and vertical line segments. The second is to report all points enclosures occurring in a mixed set of points and rectangles, and the third is to find all pairwise intersections in a set of isooriented rectangles. We derive divide-and-conquer algorithms for the first two problems which are then combined to solve the third. In each case a space-and time-optimal algorithm is obtained, that is O(n) space and O(n log n + k) time, where n is the number of given objects and k is the number of reported pairs. These results show that divide-and-conquer can be used in place of line sweep, without additional asymptotic cost, for some geometrical problems. This raises the natural question: For which class of problems are the line sweep and divide-and-conquer paradigms interchangeable?