Sparse prefix sums: Constant-time range sum queries over sparse multidimensional data cubes

Prefix sums are a powerful technique to answer range-sum queries over multi-dimensional arrays in O(1) time by looking up a constant number of values in an array of size O(N), where N is the number of cells in the multi-dimensional array. However, the technique suffers from O(N) update and storage costs. Relative prefix sums address the high update costs by partitioning the array into blocks, thereby breaking the dependency between cells.