No abstract

Mapping to one-dimensional values and then using a one-dimensional indexing method has been proposed as a way of indexing multi-dimensional data. Most previous related work uses the Z-Order Curve but more recently the Hilbert Curve has been considered since it has superior clustering properties. Any approach, however, can only be of practical value if there are effective methods for executing range and partial match queries. This paper describes such a method for the Hilbert Curve.

The Hilbert Curve describes a method of mapping between one and n dimensions. Such mappings are of interest in a number of application domains including image processing and, more recently, in the indexing of multi-dimensional data. Relatively little work, however, has been devoted to techniques for mapping in more that 2 dimensions. This paper presents a technique for constructing state diagrams to facilitate mappings and is a specialization of an incomplete generic process described by Bially. Although the storage requirements for state diagrams increase exponentially with the number of dimensions, they are useful in up to about 9 dimensions.