Dynamic point location in fat hyperrectangles with integer coordinates

A data structure is presented for point location in a disjoint set of hyperrectangles in arbitrary fixed dimension with integer coordinates less than U . Point location query times are O(log logU), in any dimension. The space and construction costs are dependent of the fatness of the hyperrectangles stored in the structure. The fatness of a hyperrectangle x is defined to be the size of the smallest set of hypercubes whose union is x. Given a set of n hyperrectangles with average fatness f the time to construct the data structure is O(fn logU log logU) randomized, and the structure will use O(fn log logU) space. Semidynamic and fully dynamic variants of this data structure are also presented.