On Counting Range Maxima Points in Plane

Abstract

We consider the problem of reporting and counting maximal points in a given orthogonal query range in two-dimensions. Our model of computation is the pointer machine model. Let P be a static set of n points in ℝ2. A point is maximal in P if it is not dominated by any other point in P. We propose a linear space data structure that can support counting the number of maximal points inside a 3-sided orthogonal query rectangle unbounded on its right in O(logn) time. For counting the number of maximal points in a 4-sided orthogonal query rectangle, we propose an O(n logn) space data structure that can be constructed in O(n logn) time and queried upon in O(logn) time. This work proposes the first data structure for counting the number of maximal points in a query range. Das et al. proposed a data structure for the counting version in the word RAM model [WALCOM 2012].