Compact Hilbert Indices for Multi-Dimensional Data
Space-filling curves, particularly Hilbert curves, have proven to be a powerful paradigm for maintaining spatial groupings of multi-dimensional data in a variety of application areas including database systems, data structures and distributed information systems. One significant limitation in the standard definition of Hilbert curves is the requirement that the grid size (i.e. the cardinality) in each dimension be the same. In the real world, not all dimensions are of equal size and the work-around of padding all dimensions to the size of the largest dimension wastes memory and disk space, while increasing the time spent manipulating and communicating these \"Inflated\" values.