Dynamic orthogonal range queries in OLAP

Abstract

We study the problem of pre-computing auxillary information to support on-line range queries for the sum and max functions on a datacube. For a d-dimensional datacube with size n in each dimension, we propose a dynamic range max data structure with O( α d ( s, n) L d ) query time, O( α d ( s, n) L 2 d n d/ L ) update time and O( s d ) storage where L and s are parameters chosen by the user before the construction of the data structure such that L∈{1,…,⌈ log n⌉} and s is a non-negative multiple of n; and α( s, n) is the functional inverse of Ackermann's function. Moreover, the data structure can be initialized in time linear to its size. There are three major techniques employed in designing the data structure, namely, a technique for trading query and update times, a technique for trading query time and storage and a technique for extending one-dimensional data structures to d-dimensional ones. Our techniques are also applicable to range queries over any semigroup and group operation, such as min, sum and count.