Efficient external memory structures for range-aggregate queries

We present external memory data structures for efficiently answering range-aggregate queries. The range-aggregate problem is defined as follows: Given a set of weighted points in R, compute the aggregate of the weights of the points that lie inside a d-dimensional orthogonal query rectangle. The aggregates we consider in this paper include COUNT, SUM, and MAX. First, we develop a structure for answering two-dimensional range-COUNT queries that uses O(N/B) disk blocks and answers a query in O(logB N) I/Os, where N is the number of input points and B is the disk block size. The structure can be extended to obtain a near-linear-size structure for answering range-SUM queries usingO(logB N) I/Os, and a linear-size structure for answering range-MAX queries in O(log2B N) I/Os. Our structures can be made dynamic and extended to higher dimensions.