On the quality of partitions based on space-filling curves

Abstract

This paper presents bounds on the quality of partitions induced by space-filling curves. We compare the surface that surrounds an arbitrary index range with the optimal partition in the grid, i. e. the square. It is shown that partitions induced by Lebesgue and Hilbert curves behave about 1.85 times worse with respect to the length of the surface. The Lebesgue indexing gives better results than the Hilbert indexing in worst case analysis. Furthermore, the surface of partitions based on the Lebesgue indexing are at most 5/2·√3 times larger than the optimal in average case. © Springer-Verlag 2002.