Space-Filling Curves for Query Processing
Distance-preserving mapping; Linearization; Locality-preserving mapping; Multidimensional mapping
Given a query Q, a one-dimensional index structure I (e.g., B-tree), and a set of D-dimensional points, a space-filling curve S is used to map the D-dimensional points into a set of one-dimensional points that can be indexed through I for an efficient execution of query Q. The main idea is that space-filling curves are used as a way of mapping the multidimensional space into the one-dimensional space such that existing one-dimensional query processing and indexing techniques can be applied.
Although space-filling curves were discovered in 1890 , their use in query processors has emerged only in the last two decades as it is mainly motivated by the emergence of multidimensional applications. In particular, space-filling curves have been used as a mapping scheme that supports spatial join algorithms , spatial access methods [2, 7], efficient...
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