大规模作战仿真空间索引技术综述

doi:10.16182/j.issn1004731x.joss.26-0222

摘要/Abstract

摘要：

大规模作战仿真的实时性与可扩展性受制于海量动态实体引发的空间查询性能瓶颈，空间索引技术通过建立位置与实体的高效映射成为破解该问题的关键。综述了大规模作战仿真中的空间索引技术，在分析作战仿真对索引结构核心要求的基础上，以静态索引、动态优化和分布式并行为主线梳理了各类索引技术的原理、演进与适用边界，并对比其查询/更新性能与内存开销。剖析了当前索引技术面临的核心矛盾并提出未来发展方向。

关键词: 空间索引, 网格索引, 作战仿真, 仿真效率

Abstract:

The real-time performance and scalability of large-scale combat simulations are constrained by performance bottlenecks in spatial queries caused by massive numbers of dynamic entities. Spatial indexing technology becomes the key to solving this problem by establishing an efficient mapping between locations and entities. This paper reviews spatial indexing technologies in large-scale combat simulations. Based on an analysis of the core requirements for index structures in combat simulations, various indexing technologies along three main lines are examined: static indexing, dynamic optimization, and distributed parallelism. The principles, evolution, and applicability boundaries of these technologies are also examined, and their query and update performance and memory overhead are compared. Finally, the core contradictions facing current indexing technologies are analyzed and future development directions are proposed.

Key words: spatial indexing, grid index, combat simulation, simulation efficiency

中图分类号:

TP391.9

靳凯迪,刘逊韵,周东傲等 . 大规模作战仿真空间索引技术综述[J]. 系统仿真学报, 2026, 38(8): 2206-2222.

Jin Kaidi,Liu Xunyun,Zhou Dongao,et al . A Review of Spatial Indexing Technologies for Large-scale Combat Simulation[J]. Journal of System Simulation, 2026, 38(8): 2206-2222.

图/表 8

图1

表1

图2

图3

图4

表2

静态索引技术性能对比

经典索引	空间复杂度	构建	范围查询(平均/最坏)	单次插入/删除
PR四叉树^[35]	O(n)	O(nlog n)	O(k+m)/O(n)	O(log $M$ )
KD-Tree^[25]	O(n)	O(nlog n)	O(k+n^1–1/^d )/O(n)	O(log n)
R-Tree^[10]	O(n)~ O(nlog n)	O(nlog n)	O(k+log n)/O(n)	O(log n)
QR-Tree^[41]	O(n)	O(nlog n)	O(k+log n)/O(n)	O(log n)
Ldex^[44]	O(n+M)	O(n)	O(k+m)/O(n)	O(1)
二级网格^[52]	O(n+M)	O(n)	O(k+m)/O(n)	O(1)
LUGrid^[57]	O(n+M)	O(n)	O(k+m)/O(n)	O(1)
HSIBGR^[61]	O(n)	O(nlog n_avg)	O(k+m log n_avg)/O(n)	O(log n_avg)
ML-Index^[65]	O(qd+H)	O(qndi+ nlog n)	O(k+qd+Hlog(e))/O(n)	不支持

表2

表3

静态索引技术特点与使用场景对比

索引类型	数据结构与核心特点	优劣势	典型适用场景	参考文献
四叉树	规则递归四分裂，结构简单	实现简单，与空间对象分布相适应，方便多维扩展；实体规模增加，树深差异影响空间利用率	适合处理分布均匀的圆形或矩形范围查询(如通信连通性等)	[2,16,23,36,55]
KD-Tree	二叉树，循环选择维度划分	点目标查询高效，存储空间需求小；动态更新成本高	支持K近邻查询(如路径规划等)	[23,25,36,66]
R-Tree	基于MBR的层次包围盒	范围查询好，支持动态更新；节点重叠影响性能	可以表示不规则形状实体和区域(如火力覆盖区、雷达探测区)	[10,16,23,36,55]
QR-Tree	顶层四叉树全局划分，底层R-Tree	兼顾查询效率与动态性；结构更复杂，开销增加	具备四叉树与R-Tree的特点，适合高动态、大规模查询(如碰撞检测、雷达探测)	[23,36,41]
单级网格	均匀划分的规则单元格阵列	查询速度快；稀疏时内存浪费严重	适合实体均匀分布、内存充足的高频更新场景(如通信连通性)	[23,31,36,44-45]
多级网格	分层级的多分辨率网格	内存利用率高，支持多尺度查询；需维护层级关系	适合需同时进行粗粒度与细粒度查询的场景(如通信连通性)	[23,52]
自适应网格	网格单元依据实体分布动态调整	内存利用率高，查询精度高；构建与维护算法复杂	适合实体分布极度不均、存在密集热点的场景(如雷达探测、路径规划)	[23,52]
混合索引	融合树与网格等多种结构优势	平衡查询与更新性能；设计复杂，需针对性优化	需求复杂的综合场景(如火力覆盖、雷达探测、碰撞检测)	[36,57]
学习型索引	机器学习模型解决索引问题	能自动从数据与查询中学习，不依赖人工设定规则参数；实时动态更新和多边形、轨迹等复杂空间对象支持困难	中高维目标特征索引和静态目标数据的检索(如静态下的威胁评估)	[18,64-65,67]

表3

图5

参考文献 87

[1]	吕雁. 计算机仿真与建模技术综述[J]. 电子科技, 2001(11): 2-4.
[2]	吕亮, 施群山, 蓝朝桢, 等. 基于轨道约束的空间目标球面网格索引及区域查询应用[J]. 计算机应用, 2017, 37(7): 2095-2099.
	Liang Lü, Shi Qunshan, Lan Chaozhen, et al. Space Target Sphere Grid Index Based on Orbit Restraint and Region Query Application[J]. Journal of Computer Applications, 2017, 37(7): 2095-2099.
[3]	Wagenbreth G, Yao K T, Davis D M, et al. Enabling 1,000,000-entity Simulations on Distributed Linux Clusters[C]//Proceedings of the Winter Simulation Conference, 2005. Piscataway: IEEE, 2005: 1-12.
[4]	Pecot I. Integrating Psychological Operations into the Joint Theater Level Simulation (JTLS)[R]. Wright-Patterson AFB, OH: Air Force Institute of Technology, 1993.
[5]	Maxwell D T. An Overview of the Joint Warfare System (JWARS)[R]. [2026-02-04]. https://www.mitre.org/sites/default/files/pdf/maxwell_jwars.pdf.
[6]	李豪, 叶帅, 史培腾, 等. 作战并行仿真技术综述[J]. 计算机科学, 2024, 51(增2): 634-640.
	Li Hao, Ye Shuai, Shi Peiteng, et al. Survey of Combat Parallel Simulation Technology[J]. Computer Science, 2024, 51(S2): 634-640.
[7]	Samet H. Foundations of Multidimensional and Metric Data Structures[M]. San Francisco: Morgan Kaufmann, 2006.
[8]	Gowanlock M. Hybrid KNN-join: Parallel Nearest Neighbor Searches Exploiting CPU and GPU Architectural Features[J]. Journal of Parallel and Distributed Computing, 2021, 149: 119-137.
[9]	蒋捷, 韩刚, 陈军. 导航地理数据库[M]. 北京: 科学出版社, 2003.
[10]	Guttman A. R-trees: A Dynamic Index Structure for Spatial Searching[C]//Proceedings of the 1984 ACM SIGMOD International Conference on Management of Data. New York: ACM, 1984: 47-57.
[11]	Sellis Timos K, Roussopoulos N, Faloutsos C. The R+-tree: A Dynamic Index for Multi-dimensional Objects[C]//Proceedings of the 13th International Conference on Very Large Data Bases. San Francisco: Morgan Kaufmann Publishers Inc., 1987: 507-518.
[12]	Beckmann Norbert, Kriegel Hans-Peter, Schneider Ralf, et al. The R*-tree: An Efficient and Robust Access Method for Points and Rectangles[C]//Proceedings of the 1990 ACM SIGMOD International Conference on Management of Data. New York: ACM, 1990: 322-331.
[13]	Kamel Ibrahim, Faloutsos C. Hilbert R-tree: An Improved R-tree Using Fractals[C]//Proceedings of the 20th International Conference on Very Large Data Bases. San Francisco: Morgan Kaufmann Publishers Inc., 1994: 500-509.
[14]	Pfoser D, Jensen Christian S, Theodoridis Yannis. Novel Approaches in Query Processing for Moving Object Trajectories[C]//Proceedings of the 26th International Conference on Very Large Data Bases. San Francisco: Morgan Kaufmann Publishers Inc., 2000: 395-406.
[15]	He Zhenwen, Kraak Menno-Jan, Huisman Otto, et al. Parallel Indexing Technique for Spatio-temporal Data[J]. ISPRS Journal of Photogrammetry and Remote Sensing, 2013, 78: 116-128.
[16]	周芹, 钟耳顺, 黄耀欢, 等. 大型空间数据库的并发索引策略CQR树[J]. 武汉大学学报(信息科学版), 2009, 34(7): 856-858, 863.
	Zhou Qin, Zhong Ershun, Huang Yaohuan, et al. CQR-tree: Concurrent Strategy for Spatial Index Structure in Spatial Database[J]. Geomatics and Information Science of Wuhan University, 2009, 34(7): 856-858, 863.
[17]	向隆刚, 高萌, 王德浩, 等. Geohash-trees: 一种用于组织大规模轨迹的自适应索引[J]. 武汉大学学报(信息科学版), 2019, 44(3): 436-442.
	Xiang Longgang, Gao Meng, Wang Dehao, et al. Geohash-trees: An Adaptive Index Which Can Organize Large-scale Trajectories[J]. Geomatics and Information Science of Wuhan University, 2019, 44(3): 436-442.
[18]	Nathan V, Ding Jialin, Alizadeh M, et al. Learning Multi-dimensional Indexes[C]//Proceedings of the 2020 ACM SIGMOD International Conference on Management of Data. New York: ACM, 2020: 985-1000.
[19]	Gu Tu, Feng Kaiyu, Cong Gao, et al. The RLR-tree: A Reinforcement Learning Based R-tree for Spatial Data[J]. Proceedings of the ACM on Management of Data, 2023, 1(1): 63.
[20]	Wang Lijun, Hu Linshu, Fu Chenhua, et al. SLBRIN: A Spatial Learned Index Based on BRIN[J]. ISPRS International Journal of Geo-Information, 2023, 12(4): 171.
[21]	薛忠斌, 周烜, 王珊. 双流模式下高吞吐量移动对象范围查询算法[J]. 软件学报, 2015, 26(10): 2631-2643.
	Xue Zhongbin, Zhou Xuan, Wang Shan. Throughput Oriented Range Query Algorithm for Moving Objects in Dual Stream Mode[J]. Journal of Software, 2015, 26(10): 2631-2643.
[22]	王浩宇, 龚光红, 蔡继红, 等. 基于战场元宇宙的动态三维场景感知[J]. 系统仿真学报, 2023, 35(10): 2262-2278.
	Wang Haoyu, Gong Guanghong, Cai Jihong, et al. Dynamic 3D Scene Perception Based on Battlefield Metaverse[J]. Journal of System Simulation, 2023, 35(10): 2262-2278.
[23]	陈俊杰, 朱维, 王宪锴, 等. 空间索引技术及其GIS应用综述[J]. 地理与地理信息科学, 2024, 40(2): 1-10.
	Chen Junjie, Zhu Wei, Wang Xiankai, et al. A Review of Spatial Index and Its Applications in GIS[J]. Geography and Geo-Information Science, 2024, 40(2): 1-10.
[24]	Wireland F, Carnes D, Schultz G. Using Quad Trees for Parallelizing Conflict Detection in a Sequential Simulation[C]//Proceedings 15th Workshop on Parallel and Distributed Simulation. Piscataway: IEEE, 2001: 117-123.
[25]	Bentley J L. Multidimensional Binary Search Trees Used for Associative Searching[J]. Communications of the ACM, 1975, 18(9): 509-517.
[26]	Nam Moohyeon, Kim Jinwoong, Nam Beomseok. Parallel Tree Traversal for Nearest Neighbor Query on the GPU[C]//2016 45th International Conference on Parallel Processing (ICPP). Piscataway: IEEE, 2016: 113-122.
[27]	张翀, 肖卫东, 杨晓亮, 等. 战场环境中面向范围查询的分布式时空索引[J]. 计算机工程与应用, 2011, 47(11): 118-122.
	Zhang Chong, Xiao Weidong, Yang Xiaoliang, et al. Distributed Spatio-temporal Indexing for Range Query in Battlefield[J]. Computer Engineering and Applications, 2011, 47(11): 118-122.
[28]	任春艳, 刘颖, 张迁, 等. 2022年国外高超声速空面导弹发展动态研究[J]. 航空兵器, 2023, 30(6): 18-26.
	Ren Chunyan, Liu Ying, Zhang Qian, et al. Research on Foreign Air-to-ground Hypersonic Missile Development in 2022[J]. Aero Weaponry, 2023, 30(6): 18-26.
[29]	程昌秀. 矢量数据多尺度空间索引方法的研究[J]. 武汉大学学报(信息科学版), 2009, 34(5): 597-601.
	Cheng Changxiu. A Multi-scale Spatial Index Method[J]. Geomatics and Information Science of Wuhan University, 2009, 34(5): 597-601.
[30]	Dittrich Jens, Blunschi Lukas, Vaz Salles M A. MOVIES: Indexing Moving Objects by Shooting Index Images[J]. GeoInformatica, 2011, 15(4): 727-767.
[31]	马永强, 陈晓萌, 于自强. 分布式环境下大规模移动对象范围查询算法[J]. 计算机应用, 2023, 43(1): 111-121.
	Ma Yongqiang, Chen Xiaomeng, Yu Ziqiang. Range Query Algorithm for Large Scale Moving Objects in Distributed Environment[J]. Journal of Computer Applications, 2023, 43(1): 111-121.
[32]	Finkel R A, Bentley J L. Quad Trees a Data Structure for Retrieval on Composite keys[J]. Acta Informatica, 1974, 4(1): 1-9.
[33]	Samet H. The Quadtree and Related Hierarchical Data Structures[J]. ACM Computing Surveys, 1984, 16(2): 187-260.
[34]	Ramakrishnan R, Gehrke J. Database Management Systems[M]. New York: McGraw-Hill, 2003.
[35]	Shaffer C. The PR Quadtree[M/OL]//OpenDSA Data Structures and Algorithms. Blacksburg: OpenDSA Project. (2017-01-02) [2026-01-28]. .
[36]	郑坤, 朱良峰, 吴信才, 等. 3D GIS空间索引技术研究[J]. 地理与地理信息科学, 2006, 22(4): 35-39.
	Zheng Kun, Zhu Liangfeng, Wu Xincai, et al. Study on Spatial Indexing Techniques for 3D GIS[J]. Geography and Geo-Information Science, 2006, 22(4): 35-39.
[37]	Qian Chunyao, Yi Chao, Cheng Chengqi, et al. GeoSOT-based Spatiotemporal Index of Massive Trajectory Data[J]. ISPRS International Journal of Geo-Information, 2019, 8(6): 284.
[38]	Liu Hong, Yan Jining, Wang Jinlin, et al. HGST: A Hilbert-GeoSOT Spatio-temporal Meshing and Coding Method for Efficient Spatio-temporal Range Query on Massive Trajectory Data[J]. ISPRS International Journal of Geo-Information, 2023, 12(3): 113.
[39]	Robinson J T. The K-D-B-tree: A Search Structure for Large Multidimensional Dynamic Indexes[C]//Proceedings of the 1981 ACM SIGMOD International Conference on Management of Data. New York: ACM, 1981: 10-18.
[40]	Berchtold S, Keim Daniel A, Kriegel Hans-Peter. The X-tree: An Index Structure for High-dimensional Data[C]//Proceedings of the 22th International Conference on Very Large Data Bases. San Francisco: Morgan Kaufmann Publishers Inc., 1996: 28-39.
[41]	Fu Yuchen, Hu Zhiyong, Guo Wei, et al. QR-tree: A Hybrid Spatial Index Structure[C]//Proceedings of the 2003 International Conference on Machine Learning and Cybernetics. Piscataway: IEEE, 2003: 459-463.
[42]	邱建华, 唐学兵, 黄华国. 一种基于四叉树和R-树的索引结构-QR-树[J]. 计算机应用, 2003, 23(8): 124-126, 152.
	Qiu Jianhua, Tang Xuebing, Huang Huaguo. An Index Structure Based Quad-tree and R* -tree - QR* -tree[J]. Computer Applications, 2003, 23(8): 124-126, 152.
[43]	阎超德, 赵学胜. GIS空间索引方法述评[J]. 地理与地理信息科学, 2004, 20(4): 23-26, 39.
	Yan Chaode, Zhao Xuesheng. The Review of Spatial Indexes in GIS[J]. Geography and Geo-Information Science, 2004, 20(4): 23-26, 39.
[44]	肖伟器, 冯玉才, 缪勇武. 空间对象数据库的网格索引机制[J]. 计算机学报, 1994, 17(10): 736-742.
	Xiao Weiqi, Feng Yucai, Miao Yongwu. Lattice Index Mechanism in Spatial Object Database System[J]. Chinese Journal of Computers, 1994, 17(10): 736-742.
[45]	Šidlauskas Darius, Šaltenis Simonas, Jensen Christian S. Parallel Main-memory Indexing for Moving-object Query and Update Workloads[C]//Proceedings of the 2012 ACM SIGMOD International Conference on Management of Data. New York: ACM, 2012: 37-48.
[46]	孟妮娜, 周校东. 固定格网划分的空间索引的实现技术[J]. 北京测绘, 2003(1): 7-11.
	Meng Nina, Zhou Xiaodong. Realization on Spatial Index with Grids of Fixed Size[J]. Beijing Surveying and Mapping, 2003(1): 7-11.
[47]	Gibson L, Lucas D. Spatial Data Processing Using Generalized Balanced Ternary[C]//Proceedings of the IEEE Conference on Pattern Recognition and Image Processing. Piscataway: IEEE, 1982: 566-571.
[48]	Watson A B, Ahumada A J Jr. A Hexagonal Orthogonal-oriented Pyramid as a Model of Image Representation in Visual Cortex[J]. IEEE Transactions on Biomedical Engineering, 1989, 36(1): 97-106.
[49]	童晓冲, 贲进, 张永生. 全球多分辨率六边形网格剖分及地址编码规则[J]. 测绘学报, 2007, 36(4): 428-435.
	Tong Xiaochong, Jin Ben, Zhang Yongsheng. The Subdivision of Global Multi-resolution Hexagonal Grid and the Rules of Address Coding[J]. Acta Geodaetica et Cartographica Sinica, 2007, 36(4): 428-435.
[50]	Brodsky I. H3: Hexagonal Hierarchical Geospatial Indexing System[EB/OL]. [2026-04-30]. .
[51]	吴婷婷, 吴琳, 沈弼龙. 基于H3空间索引的兵棋战场环境建模与应用探析[J]. 指挥控制与仿真, 2021, 43(5): 14-21.
	Wu Tingting, Wu Lin, Shen Bilong. Battlefield Environment Modeling and Application Research in Wargame Based on H3 Spatial Index[J]. Command Control & Simulation, 2021, 43(5): 14-21.
[52]	胡久乡, 何松, 钟瑜. 空间数据库网格索引机制的最优划分[J]. 计算机学报, 2002, 25(11): 1227-1230.
	Hu Jiuxiang, He Song, Zhong Yu. Optimum Mesh-indexing for Spatial Database[J]. Chinese Journal of Computers, 2002, 25(11): 1227-1230.
[53]	史绍雨, 唐新明, 吴凡, 等. 多级格网时空索引[J]. 测绘科学, 2006, 31(3): 54-55.
	Shi Shaoyu, Tang Xinming, Wu Fan, et al. Multi-level Grid Spatio-temporal Index[J]. Science of Surveying and Mapping, 2006, 31(3): 54-55.
[54]	周勇, 何建农, 涂平. 自动调配的层次网格空间索引技术[J]. 计算机应用, 2005, 25(6): 1401-1404.
	Zhou Yong, He Jiannong, Tu Ping. Technique of Auto-selection Multi-layers Grid Spatial Index[J]. Journal of Computer Applications, 2005, 25(6): 1401-1404.
[55]	李德仁, 朱欣焰, 龚健雅. 从数字地图到空间信息网格-空间信息多级网格理论思考[J]. 武汉大学学报(信息科学版), 2003, 28(6): 642-650.
	Li Deren, Zhu Xinyan, Gong Jianya. From Digital Map to Spatial Information Multi-grid—A Thought of Spatial Information Multi-grid Theory[J]. Geomatics and Information Science of Wuhan University, 2003, 28(6): 642-650.
[56]	Legras François, Fujino Iwao, Thierry Le Pors, et al. Introducing KH3: A Frugal Trajectory Indexing System[C]//OCEANS 2025 Brest. Piscataway: IEEE, 2025: 1-6.
[57]	Xiong Xiaopeng, Mokbel M F, Aref W G. LUGrid: Update-tolerant Grid-based Indexing for Moving Objects[C]//7th International Conference on Mobile Data Management (MDM'06). Piscataway: IEEE, 2006: 13-13.
[58]	Huang Weizhang, Russell Robert D. Adaptive Moving Mesh Methods[M]. New York: Springer, 2011.
[59]	王映辉. 一种GIS自适应层次网格空间索引算法[J]. 计算机工程与应用, 2003, 39(9): 58-60.
	Wang Yinghui. An Algorithm of Self-adaptation Layer-grid Spatial Index[J]. Computer Engineering and Applications, 2003, 39(9): 58-60.
[60]	Du Jinchun, Shen Bojie, Zhao Shizhe, et al. Efficient Object Search in Game Maps[C]//Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence. Palo Alto: AAAI Press, 2023: 5567-5576.
[61]	吴敏君, 郭永洪, 陈天滋. 一种有效的混合空间索引机制[J]. 计算机工程与应用, 2006, 42(29): 193-197.
	Wu Minjun, Guo Yonghong, Chen Tianzi. Efficient Hybrid Structure of Spatial Index for GIS Databases[J]. Computer Engineering and Applications, 2006, 42(29): 193-197.
[62]	周侗, 龙毅, 汤国安, 等. 面向集聚分布空间数据的混合式索引方法研究[J]. 地理与地理信息科学, 2010, 26(1): 7-10.
	Zhou Dong, Long Yi, Tang Guoan, et al. Research on the Hybrid Index Structure for Aggregated Spatial Data[J]. Geography and Geo-Information Science, 2010, 26(1): 7-10.
[63]	Kraska T, Beutel A, Chi E H, et al. The Case for Learned Index Structures[C]//Proceedings of the 2018 International Conference on Management of Data. New York, NY, USA: ACM, 2018: 489-504.
[64]	Ding Jialin, Nathan V, Alizadeh M, et al. Tsunami: A Learned Multi-dimensional Index for Correlated Data and Skewed Workloads[J]. Proceedings of the VLDB Endowment, 2020, 14(2): 74-86.
[65]	Davitkova A, Milchevski E, Michel S. The ML-index: A Multidimensional, Learned Index for Point, Range, and Nearest-neighbor Queries[C]//EDBT. [S.l.: s.n.], 2020: 407-410.
[66]	Yu Ziqiang, Xhafa Fatos, Chen Yuehui, et al. A Distributed Hybrid Index for Processing Continuous Range Queries Over Moving Objects[J]. Soft Computing, 2019, 23(9): 3191-3205.
[67]	Li Pengfei, Lu Hua, Zheng Qian, et al. LISA: A Learned Index Structure for Spatial Data[C]//Proceedings of the 2020 ACM SIGMOD International Conference on Management of Data. New York: ACM, 2020: 2119-2133.
[68]	Tang Jine, Zhou Zhangbing, Ning Ke, et al. A Novel Spatial Indexing Mechanism Leveraging Dynamic Quad-tree Regional Division[C]//Proceedings of the 2012 International Conference on Information Technology and Software Engineering. Berlin: Springer, 2013: 909-917.
[69]	Teschner M, Heidelberger B, Müller M, et al. Optimized Spatial Hashing for Collision Detection of Deformable Objects[C]//Proceedings of the 2003 Vision, Modeling, and Visualization Conference. Stuttgart: Akademische Verlagsgesellschaft, 2003: 47-54.
[70]	Chaudhry Natalia, Muhammad Murtaza Yousaf. A Hash-based Index for Processing Frequent Updates and Continuous Location-based Range Queries[J]. Knowledge and Information Systems, 2023, 65(10): 4233-4271.
[71]	Shin Jaewoo, Mahmood A R, Aref Walid G. An Investigation of Grid-enabled Tree Indexes for Spatial Query Processing[C]//Proceedings of the 27th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems. New York: ACM, 2019: 169-178.
[72]	Dong Haowen, Chai Chengliang, Luo Yuyu, et al. RW-tree: A Learned Workload-aware Framework for R-tree Construction[C]//2022 IEEE 38th International Conference on Data Engineering (ICDE). Piscataway: IEEE, 2022: 2073-2085.
[73]	Hu Haibo, Xu Jianliang, Lun Lee Dik. A Generic Framework for Monitoring Continuous Spatial Queries Over Moving Objects[C]//Proceedings of the 2005 ACM SIGMOD International Conference on Management of Data. New York: ACM, 2005: 479-490.
[74]	Mouratidis Kyriakos, Bakiras S, Papadias Dimitris. Continuous Monitoring of Spatial Queries in Wireless Broadcast Environments[J]. IEEE Transactions on Mobile Computing, 2009, 8(10): 1297-1311.
[75]	Hojati Majid, Roberts Steven, Robertson Colin. DSTree: A Spatio-temporal Indexing Data Structure for Distributed Networks[J]. Mathematical and Computational Applications, 2024, 29(3): 42.
[76]	秦学程, 刘春颜, 李宝, 等. 面向工业场景的云边协同数据存储与检索架构[J]. 计算机应用, 2025, 45(9): 2902-2912.
	Qin Xuecheng, Liu Chunyan, Li Bao, et al. Cloud-edge Collaborative Data Storage and Retrieval Architecture for Industrial Scenarios[J]. Journal of Computer Applications, 2025, 45(9): 2902-2912.
[77]	Liu Xianglong, Wang Hongzhi, Li Yingze, et al. Crame: Hierarchical Data Management Framework for Cloud-edge-device Collaboration[J]. Information Sciences, 2026, 740: 123197.
[78]	陈景广, 佘江峰, 宋晓群, 等. 基于多核CPU的大规模DEM并行三维渲染[J]. 武汉大学学报(信息科学版), 2013, 38(5): 618-621.
	Chen Jingguang, She Jiangfeng, Song Xiaoqun, et al. Parallel Rendering of Large-scale DEM Based on Multi-core CPU[J]. Geomatics and Information Science of Wuhan University, 2013, 38(5): 618-621.
[79]	Salam Abdul, Jamil Safdar, Jung Sungwon, et al. Future-based Persistent Spatial Data Structure for NVM-based Manycore Machines[J]. IEEE Access, 2022, 10: 114711-114724.
[80]	赵亮, 陈荦, 景宁, 等. 一种高效的移动对象连续多范围查询处理框架[C]//第26届中国数据库学术会议论文集(B辑). 北京: 科学出版社, 2009: 211-217.
	Zhao Liang, Chen Luo, Jing Ning, et al. An Efficient Framework for Processing Continuous Multiple Range Queries on Moving Objects[C]//Proceedings of the 26th Chinese Database Conference (Volume B). Beijing: Science Press, 2009: 211-217.
[81]	Kunjir M, Manthramurthy A. Using Graphics Processing in Spatial Indexing Algorithms[R]. Bangalore: Indian Institute of Science, Database Systems Lab, 2009.
[82]	Prasad S K, Mcdermott M, He Xi, et al. GPU-based Parallel R-tree Construction and Querying[C]//2015 IEEE International Parallel and Distributed Processing Symposium Workshop. Piscataway: IEEE, 2015: 618-627.
[83]	Jackowiak Bogdan, Lawenda Marcin. How Does Sharing Data from Research Institutions on Global Biodiversity Information Facility Enhance Its Scientific Value?[J]. Diversity, 2025, 17(4): 221.
[84]	Grosser Tobias, Cohen Albert, Holewinski Justin, et al. Hybrid Hexagonal/Classical Tiling for GPUs[C]//Proceedings of Annual IEEE/ACM International Symposium on Code Generation and Optimization. New York: ACM, 2018: 66-75.
[85]	García Francisco M, Kapadia M, Badler N I. GPU-based Dynamic Search on Adaptive Resolution Grids[C]//2014 IEEE International Conference on Robotics and Automation (ICRA). Piscataway: IEEE, 2014: 1631-1638.
[86]	Gallet B, Gowanlock M. Heterogeneous CPU-GPU Epsilon Grid Joins: Static and Dynamic Work Partitioning Strategies[J]. Data Science and Engineering, 2021, 6(1): 39-62.
[87]	赵艳伟, 于璐, 张宁, 等. 一种基于GPGPU的指控系统空间查询优化方法[J]. 指挥与控制学报, 2015, 1(4): 395-402.
	Zhao Yanwei, Yu Lu, Zhang Ning, et al. An Optimized Spatial Search Method Based on GPGPU for Command and Control Systems[J]. Journal of Command and Control, 2015, 1(4): 395-402.

典型业务场景	查询类型	查询特征
雷达/声呐探测^[21]	范围查询	扇形/圆锥
通视计算^[22]	射线查询	线段/射线
火力覆盖分析^[23]	区域查询	任意多边形
碰撞检测^[24]	近邻查询	球形/包围盒
路径规划^[25]	范围查询	矩形/圆形
威胁评估^[26]	K近邻查询	圆形(返回k个最近)
通信连通性^[22]	距离查询	圆形(阈值判定)