Optimal Range Max Datacube for Fixed Dimensions

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 O(c1d) 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 fixed, i.e., a constant independent of n.

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