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Space filling curves (SFCs) are widely used in the design of indexes forspatial and temporal data. Clustering is a key metric for an SFC, that measureshow well the curve preserves locality in moving from higher dimensions to asingle dimension. We present the {\em onion curve}, an SFC whose clusteringperformance is provably close to optimal for the cube and near-cube shapedquery sets, irrespective of the side length of the query. We show that incontrast, the clustering performance of the widely used Hilbert curve can befar from optimal, even for cube-shaped queries. Since the clusteringperformance of an SFC is critical to the efficiency of multi-dimensionalindexes based on the SFC, the onion curve can deliver improved performance fordata structures involving multi-dimensional data.

Onion Curve: A Space Filling Curve with Near-Optimal Clustering