Conference Paper
On the Locality Properties of SpaceFilling Curves.
DOI: 10.1007/9783540245872_40 Conference: Algorithms and Computation, 14th International Symposium, ISAAC 2003, Kyoto, Japan, December 1517, 2003, Proceedings
Source: DBLP


Conference Paper: Approximation and Analytical Studies of Interclustering Performances of SpaceFilling Curves.
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ABSTRACT: A discrete spacefilling curve provides a linear traversal/indexing of a multidimensional grid space. This paper presents an application of random walk to the study of interclustering of spacefilling curves and an analytical study on the interclustering performances of 2dimensional Hilbert and zorder curve families. Two underlying measures are employed: the mean intercluster distance over all intercluster gaps and the mean total intercluster distance over all subgrids. We show how approximating the mean intercluster distance statistics of continuous multidimensional spacefilling curves fits into the formalism of random walk, and derive the exact formulas for the two statistics for both curve families. The excellent agreement in the approximate and true mean intercluster distance statistics suggests that the random walk may furnish an effective model to develop approximations to clustering and locality statistics for spacefilling curves. Based upon the analytical results, the asymptotic comparisons indicate that zorder curve family performs better than Hilbert curve family with respect to both statistics.Discrete Random Walks, DRW'03, Paris, France, September 15, 2003; 01/2003
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