Orthogonal range queries in OLAP

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 data structure for range max queries with O((4L)(d)) query time and O((12L(2)n(1/L)gamma (n))(d)) update time where L is an element of {1,..., log n} is a user-controlled parameter and gamma (n) is a slow-growing function. (For example, gamma (n) less than or equal to log*n and gamma (2(4110)) = 3.) The data structure uses O((6n gamma (n))(d)) storage and 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 1-dimensional data structures to d-dimensional ones. Our techniques are also applicable to range queries over any semi-group and group operation, such as min, sum and count.