Maintaining spatial data (points in two or three dimensions) is crucial and has a wide range of applications, such as graphics, GIS, and robotics. To handle spatial data, many data structures, called spatial indexes, have been proposed, e.g. kd-trees, oct/quadtrees (also called Orth-trees), R-trees, and bounding volume hierarchies (BVHs). In real-world applications, spatial datasets tend to be highly dynamic, requiring batch updates of points with low latency. This calls for efficient parallel batch updates on spatial indexes. Unfortunately, there is very little work that achieves this. In this paper, we systematically study parallel spatial indexes, with a special focus on achieving high-performance update performance for highly dynamic workloads. We select two types of spatial indexes that are considered optimized for low-latency updates: Orth-tree and R-tree/BVH. We propose two data structures: the P-Orth tree, a parallel Orth-tree, and the SPaC-tree family, a parallel R-tree/BVH. Both the P-Orth tree and the SPaC-tree deliver superior performance in batch updates compared to existing parallel kd-trees and Orth-trees, while preserving better or competitive query performance relative to their corresponding Orth-tree and R-tree counterparts. We also present comprehensive experiments comparing the performance of various parallel spatial indexes and share our findings at the end of the paper.

翻译：维护空间数据（二维或三维点）至关重要，在图形学、地理信息系统和机器人学等领域具有广泛应用。为处理空间数据，研究者提出了多种称为空间索引的数据结构，例如kd树、八叉树/四叉树（亦称正交树）、R树和包围体层次结构。在实际应用中，空间数据集往往高度动态，需要以低延迟进行点的批量更新，这就要求空间索引能够支持高效的并行批量更新操作。遗憾的是，现有研究在此方面成果甚少。本文系统研究了并行空间索引，特别关注在高度动态工作负载下实现高性能更新。我们选取了两类被认为针对低延迟更新优化的空间索引：正交树与R树/包围体层次结构，并提出了两种新型数据结构：并行正交树P-Orth树与并行R树/包围体层次结构家族SPaC-tree。实验表明，相较于现有并行kd树和正交树，P-Orth树与SPaC-tree在批量更新中均展现出更优性能，同时在查询性能上保持优于或持平于对应正交树与R树基准的水平。本文最后通过系统实验对比了各类并行空间索引的性能，并分享了相关研究发现。