用于球面范围查询的数据结构的基准测试与工程设计
Benchmarking and Engineering Data Structures for Spherical Range Queries
AI总结：
针对球面范围查询中选择最佳数据结构困难的问题，通过对多种基准上的现有空间索引全面评估，引入高性能SPRK-tree，它经多种优化，在多数基准测试中查询时间最快，少数情况下排名第二。
摘要：
球面范围查询是处理空间数据的基本原语。许多空间数据结构已被开发用于回答此类查询，但为特定应用选择最佳结构是一项艰巨任务。理论最坏情况边界往往过于悲观，现有平均情况分析受限且难比较。我们有两个主要贡献来解决此问题。首先，我们对各种基准上的现有空间索引进行全面评估，包括基于图嵌入的新基准和多个文献中的真实世界数据集，基准涵盖高达1000万个点且维度在2到960之间的实例。其次，我们引入了Sorted-Projection Radius KD-tree（SPRK-tree），一种高性能KD树变体。它通过半径缩减进行积极的子树修剪、基于排序投影的叶节点以及精心的实现优化。在几乎所有基准测试中它始终实现最快查询时间，在其余少数情况下排名第二。
英文摘要：
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.
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