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

TL;DR

The paper introduces the onion curve, a space filling curve with near-optimal clustering properties for multi-dimensional data, outperforming traditional curves like Hilbert in preserving locality for cube-shaped queries.

Contribution

The onion curve is a new space filling curve with provably near-optimal clustering performance for cube-shaped queries, improving multi-dimensional index efficiency.

Findings

Onion curve achieves near-optimal clustering for cube queries.

Hilbert curve's clustering can be far from optimal for similar queries.

Onion curve enhances multi-dimensional data indexing performance.

Abstract

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