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Benchmarking and Engineering Data Structures for Spherical Range Queries

Authors Thomas Bläsius , Jean-Pierre von der Heydt , Tobias Kempf , Dennis Kobert , Nikolai Maas

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Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
  • Theory of computation → Data structures design and analysis
Keywords
  • Spherical Range Queries
  • Fixed-Radius Nearest Neighbor Search
  • Spatial Indexing
  • KD-tree
  • Benchmarking
  • Graph Embedding
  • SPRK-Tree

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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.

Cite As Get BibTex

Thomas Bläsius, Jean-Pierre von der Heydt, Tobias Kempf, Dennis Kobert, and Nikolai Maas. Benchmarking and Engineering Data Structures for Spherical Range Queries. In 34th Annual European Symposium on Algorithms (ESA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 388, pp. 22:1-22:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ESA.2026.22

Author Details

Thomas Bläsius
  • Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
Jean-Pierre von der Heydt
  • Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
Tobias Kempf
  • Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
Dennis Kobert
  • Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
Nikolai Maas
  • Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany

Funding

  • von der Heydt, Jean-Pierre: This work was supported by funding from the pilot program Core-Informatics of the Helmholtz Association (HGF).

Supplementary Materials

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