OPTIMAL RANGE MAX DATACUBE FOR FIXED DIMENSIONS

Abstract

We present a new data structure to support orthogonal range max queries on a datacube. For a d-dimensional datacube with size n in each dimension where d≤c3 log log n/ log ( log * n), our structure requires [Formula: see text] query time and O((c2n)d) storage where c1, c2 and c3 are constants independent of d and n; and log * n is the minimum number of repeated logarithms it takes to reduce the value n to at most 2. Hence our data structure is asymptotically optimal when d is constant independent of n.