New results on two-dimensional orthogonal range aggregation in external memory

Abstract

We consider the orthogonal range aggregation problem. The dataset S consists of N axis-parallel rectangles in R², each of which is associated with an integer weight. Given an axis-parallel rectangle Q and an aggregate function F, a query reports the aggregated result of the weights of the rectangles in S intersecting Q. The goal is to preprocess S into a structure such that all queries can be answered efficiently. We present indexing schemes to solve the problem in external memory when F = max (hence, min) and F = sum (hence, count and average), respectively. Our schemes have linear or near-linear space, and answer a query in O(log_BN) or O(logB²/BN) I/Os, where B is the disk block size.