Benchmarking and Engineering Data Structures for Spherical Range Queries

2026-07-08

AI Summary

This work addresses the lack of efficient and general-purpose spatial indexes for spherical range queries, a problem exacerbated by overly pessimistic theoretical bounds and limited empirical analyses of average-case performance. To bridge this gap, the authors construct a comprehensive benchmark encompassing graph embeddings and diverse real-world datasets (tens of millions of points across dimensions 2–960) and systematically evaluate state-of-the-art spatial indexing methods. They propose SPRK-tree, a novel variant of the KD-tree that integrates radius-reduction pruning, sorted projected leaf nodes, and engineering optimizations. SPRK-tree achieves the fastest query performance in nearly all benchmark settings and ranks second in the remainder, consistently and significantly outperforming existing approaches, thereby demonstrating its superior efficiency and strong generalization capability.

Abstract

Spherical range queries are a fundamental primitive for working with spatial data. Many spatial data structures have been developed to answer these queries, but choosing the optimal one for a specific application is a difficult task. This is because theoretical worst-case bounds are often overly pessimistic, and existing average-case analyses are rather restricted and hard to compare. We address this problem with two main contributions. First, we present a comprehensive evaluation of state-of-the-art spatial indices across a diverse set of benchmarks. This includes a new benchmark based on graph embeddings alongside multiple real-world datasets from the literature. Our benchmark covers instances scaling up to 10M points and ranging between 2 and 960 dimensions. Second, we introduce the Sorted-Projection Radius KD-tree (SPRK-tree), a high-performance KD-tree variant. The SPRK-tree combines aggressive subtree pruning via radius reduction, sorted projection-based leaf nodes, and careful implementation optimizations. It consistently achieves the fastest query times in almost all benchmarks, and ranks second in the few remaining cases.

Problem

• spherical range queries
• spatial data structures
• benchmarking
• average-case analysis
• worst-case bounds

Innovation

• spherical range queries
• SPRK-tree
• spatial indexing
• benchmarking
• KD-tree optimization