External memory range reporting on a grid

Abstract

In this paper we present external memory data structures for orthogonal range reporting queries on a grid. Our data structure for two-dimensional orthogonal range reporting queries uses O((N/B) log2 N) blocks of space of size B and supports queries in optimal O(log2 log B U+ T/B) time, where U is the size of universe, N is the number of elements in the data structure, and T is the size of the answer. Our data structure for three-sided range reporting queries that uses O(N/B) blocks of space and supports queries in O(log2 logB U + T/B) time. In the case of three-sided range reporting on a N × ℕ grid, we describe a O((N/B) logB2 N) space data structure with O(T/B) query time, a O((N/B) logB*, N) data structure with O(logB* N + T/B) query time, and a O(N/B) space data structure with O(logB(k) N + T/B) query time for any constant k. © Springer-Verlag Berlin Heidelberg 2007.