Optimality of Clustering Properties of Space-Filling Curves

• Autores: Pan Xu, Srikanta Tirthapura
• Localización: ACM transactions on database systems, ISSN 0362-5915, Vol. 39, Nº 2, 2014
• Idioma: inglés
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• Resumen

  • Space-filling curves have been used in the design of data structures for multidimensional data for many decades. A fundamental quality metric of a space-filling curve is its “clustering number” with respect to a class of queries, which is the average number of contiguous segments on the space-filling curve that a query region can be partitioned into. We present a characterization of the clustering number of a general class of space-filling curves, as well as the first nontrivial lower bounds on the clustering number for any space-filling curve. Our results answer questions that have been open for more than 15 years.