Abstract

We consider the problem of reporting the pairwise enclosures among a set of n axes-parallel rectangles in IR 2 , which is equivalent to reporting dominance pairs in a set of n points in IR 4 . For more than ten years, it has been an open problem whether these problems can be solved faster than in O(n log 2 n+k) time, where k denotes the number of reported pairs. First, we give a divide-and-conquer algorithm that matches the O(n) space and O(n log 2 n + k) time bounds of the algorithm of Lee and Preparata [LP82], but is simpler. Then we give another algorithm that uses O(n) space and runs in O(n log n log log n+k log log n) time. For the special case where the rectangles have at most ff different aspect ratios, we give an algorithm that runs in O(ffn log n + k) time and uses O(n) space. 1 Introduction The problem of computing intersections in a set of rectangles has received much attention. (See Chapter 8 of [PS88].) There are several variants of the problem depending...

Citations