Efficient management of ubiquitous location information using geospatial grid region name 利用地理空间网格区域名称高效管理无处不在的位置信息
Daoye Zhu ^("a,b,c "){ }^{\text {a,b,c }}, Min huang ^("d,e "){ }^{\text {d,e }}, Qifeng Lin ^("a,* "){ }^{\text {a,* }}, Yanyu Wang ^("f "){ }^{\text {f }} (D), Shuang Li ^("g "){ }^{\text {g }}, Chengqi Cheng ^("b,h "){ }^{\text {b,h }} 朱道业 ^("a,b,c "){ }^{\text {a,b,c }} ，黄敏 ^("d,e "){ }^{\text {d,e }} ，林启峰 ^("a,* "){ }^{\text {a,* }} ，王燕宇 ^("f "){ }^{\text {f }} (D)，李双 ^("g "){ }^{\text {g }} ，程成奇 ^("b,h "){ }^{\text {b,h }}^("a "){ }^{\text {a }} College of Computer and Data Science, Fuzhou University, Fuzhou 350108, China ^("a "){ }^{\text {a }} 福州大学计算机与数据科学学院，福建省福州市，邮编：350108，中国^(b){ }^{\mathrm{b}} Center for Data Science, Peking University, Beijing 100871, China ^(b){ }^{\mathrm{b}} 北京大学数据科学中心，北京市海淀区中关村南大街 1 号，邮编：100871，中国^("c "){ }^{\text {c }} Department of Geography, Geomatics and Environment, University of Toronto, Mississauga L5L 1C6, Canada ^("c "){ }^{\text {c }} 多伦多大学地理、地理信息科学与环境系，密西沙加 L5L 1C6，加拿大^(d){ }^{\mathrm{d}} School of Geography and Environment, Jiangxi Normal University, Nanchang 330022, China ^(d){ }^{\mathrm{d}} 江西师范大学地理与环境学院，南昌 330022，中国^(e){ }^{\mathrm{e}} State Key Laboratory of Information Engineering in Surveying, Mapping, and Remote Sensing, Wuhan University, Wuhan 430079, China ^(e){ }^{\mathrm{e}} 武汉大学测绘与遥感信息工程国家重点实验室，武汉 430079，中国^(f){ }^{\mathrm{f}} College of Environmental and Resource Sciences, Zhejiang University, Hangzhou 310058, China ^(f){ }^{\mathrm{f}} 浙江大学环境与资源科学学院，浙江省杭州市 310058，中国^(g){ }^{g} Institute of Chinese Historical Geography, Fudan University, Shanghai 200433, China ^(g){ }^{g} 复旦大学中国历史地理研究所，上海市，中国 200433^(h){ }^{\mathrm{h}} College of Engineering, Peking University, Beijing 100871, China ^(h){ }^{\mathrm{h}} 北京大学工学院，北京市海淀区中关村南大街 1 号，邮编：100871，中国
A R T I C L E I N F O 文章信息
Keywords: 关键词：
Geospatial grid region name 地理空间网格区域名称
Ubiquitous location information 无处不在的位置信息
Geospatial region space 地理空间区域空间
Grid management 电网管理
Subdivision index big table 子分区索引大表
Abstract 摘要
With the increasing popularity of sensors and the rapid advancement of network infrastructure and communication technology, managing, retrieving, and applying ubiquitous location information (ULI) poses a significant challenge. This study introduces the concept of the geospatial grid region name (GGRN) and proposes a ULI management method based on the GGRN (UMMG). To evaluate the feasibility and retrieval efficiency of the UMMG, it was applied to mainstream databases and compared with their spatial expansion modules. The experimental results demonstrate that the UMMG effectively addresses the challenge of precise location cognition between humans and machines while also reducing the complexity of spatial database indexing, with an overall performance improvement of 43.00 % compared to Oracle Spatial and 33.30 % compared to PostgreSQL + PostGIS. 随着传感器技术的普及和网络基础设施及通信技术的快速发展，管理、检索和应用无处不在的位置信息（ULI）已成为一项重大挑战。本研究提出了地理空间网格区域名称（GGRN）的概念，并基于 GGRN 提出了一种 ULI 管理方法（UMMG）。为评估 UMMG 的可行性与检索效率，将其应用于主流数据库并对比其空间扩展模块。实验结果表明，UMMG 有效解决了人机间精准位置认知挑战，同时简化了空间数据库索引复杂度，与 Oracle Spatial 相比整体性能提升 43.00%，与 PostgreSQL + PostGIS 相比提升 33.30%。
1. Introduction 1. 引言
With the increasing popularity of various sensors and the rapid development of network infrastructure and communication technology, an increasing number of fields are collecting and accumulating large amounts of data and exploring their value (Ahalt, 2013). Consequently, the International Data Corporation predicts that the total global data volume will increase from 33 ZB in 2018 to 175 ZB in 2025 (Reinsel et al., 2019). At least 80%80 \% of data are related to spatial location ( Li and Li, 2014), and almost all phenomena contain three basic characteristics: space, time, and attributes. Therefore, the vast majority of data is ULI. ULI on the Internet, the Internet of Things, and sensor networks are exploding (Li et al., 2014), widely used in urban construction, intelligent transportation, public safety, environmental monitoring, resource management, emergency disaster relief, and other fields (Gong et al., 随着各种传感器日益普及以及网络基础设施和通信技术的快速发展，越来越多的领域开始收集和积累大量数据，并探索其价值（Ahalt，2013）。因此，国际数据公司预测，全球数据总量将从 2018 年的 33ZB 增长至 2025 年的 175ZB（Reinsel 等，2019）。其中至少 80%80 \% 的数据与空间位置相关（Li 和 Li，2014），而几乎所有现象都具备三个基本特征：空间、时间和属性。因此，绝大多数数据属于 ULI。互联网、物联网和传感器网络中的 ULI 正呈爆炸式增长（Li et al., 2014），广泛应用于城市建设、智能交通、公共安全、环境监测、资源管理、应急灾害救援等领域（Gong et al.,
2022). Significant amounts of ULI have emerged with four characteristics: large data volume, heterogeneity, fragmentation, and real-time data flow. Therefore, managing, retrieving, and applying ULI is challenging in the era of big data. （2022 年）。大量超大规模数据（ULI）涌现，其主要特征包括：数据量庞大、异构性强、碎片化严重以及实时数据流。因此，在大数据时代，对超大规模数据进行管理、检索和应用面临巨大挑战。
Traditional geographic domain name methods include positional semantic conversion, information cataloging, and industrial standards. Positional semantic conversion achieves unified location conversion through independent services such as place name address databases, place name dictionaries, and gazetteers (Goodchild and Hill, 2008). Information cataloging achieves a unified organization of information through centralized data compilation, such as metadata and cataloging databases. Industrial standards include object identification formats such as the “ID code + keywords + longitude and latitude string” used by location service providers like Google, Amap, and Baidu. These traditional methods are based on longitude and latitude position 传统地理域名方法包括位置语义转换、信息目录编目和行业标准。位置语义转换通过独立服务（如地名地址数据库、地名词典和地名词汇表）实现统一的位置转换（Goodchild 和 Hill，2008）。信息目录编制通过集中式数据编纂（如元数据和目录数据库）实现信息的一致性组织。行业标准包括对象识别格式，例如位置服务提供商（如 Google、Amap 和 Baidu）使用的“ID 代码+关键词+经纬度字符串”格式。这些传统方法基于经纬度位置信息。
Fig. 1. GGRN logical structure and spatial hierarchy. A) Logical relationship between constituent elements of and different levels of GGRNs; B) logical relationship between region names at different levels in GGRN; C) GGRN reference framework and spatial hierarchy. 图 1. GGRN 的逻辑结构与空间层次。A) GGRN 各组成要素及不同层次之间的逻辑关系；B) GGRN 中不同层次区域名称之间的逻辑关系；C) GGRN 参考框架与空间层次。
identification and cannot achieve encoding-based data registration. The problems they cause are disordered storage of spatiotemporal data, low matching efficiency, and difficulties in interaction and sharing. Therefore, this research analyzes two new solutions: the GeoWeb domain name system and the What3words system. 识别问题，且无法实现基于编码的数据注册。这些问题导致时空数据存储混乱、匹配效率低下以及交互和共享困难。因此，本研究分析了两种新的解决方案：地理网络域名系统（GeoWeb Domain Name System）和 What3words 系统。
The digital earth project at the Stanford Research Institute in the United States has proposed a spatial location-based information discovery framework, GeoWeb, which is a distributed and searchable 美国斯坦福研究院的数字地球项目提出了一个基于空间位置的信息发现框架——GeoWeb，该框架具有分布式和可搜索的特点。
metadata database (Leclerc et al., 2002; Mahdavi-Amiri et al., 2015). It includes metadata standards, distributed searchable databases in the form of DNS (Vixie, 1997) server hierarchy, and API libraries for publishing, searching, and validating metadata on servers. GeoWeb will enable Internet users to navigate, access, and visualize real-world georeferenced data without physical space or time limitations. GeoWeb is a grid domain name system, and its spatial information management and publishing system is constructed through the hierarchical domain name 元数据数据库（Leclerc 等，2002；Mahdavi-Amiri 等，2015）。它包括元数据标准、以 DNS（Vixie，1997）服务器层次结构形式分布式可搜索数据库，以及用于在服务器上发布、搜索和验证元数据的 API 库。GeoWeb 将使互联网用户能够在不受物理空间或时间限制的情况下，浏览、访问和可视化现实世界中的地理参考数据。GeoWeb 是一个网格域名系统，其空间信息管理和发布系统通过分层域名结构构建。
“.geo”. It follows the design principles of transparency in mapping relationships, relatively equal relevance of search fields, abstract query formats, standardization of external publications, multilingual descriptions of objects and servers, and privacy security. Traditional metadata, such as Dublin Core (Weibel et al., 1998; Baker and Coyle, 2009), FGDC (Di et al., 2000), or ISO/TC211 (Di, 2003), is largely a description of a specific individual data item or service. GeoWeb’s searchable metadata is fundamentally different from this, providing semantic and geographic descriptions of physical or conceptual objects that may have many different forms of representation. GeoWeb imitates the domain name management mechanism of the Internet and uses the grid method of equal longitude and latitude subdivision to build the spatial information management and publishing system. It is an implementation mode of domain name and geographic information mapping and is an extensible and open global network geographic index. However, GeoWeb only allows users to access the domain name of the threelevel grid according to its specified longitude and latitude, which lacks intuition. For example, when users want to access data from a certain administrative region, GeoWeb access is difficult to implement. GeoWeb does not have a unified model for spatial data identification. It logically organizes data in the same geographical range. Thus, it does not resolve the issue of exchanging and sharing multi-source spatial data due to differing identifications. “.geo”。它遵循了映射关系透明性、搜索字段相对等同的重要性、抽象查询格式、外部出版物标准化、对象和服务器多语言描述以及隐私安全等设计原则。传统元数据，如都柏林核心元数据（Dublin Core，Weibel 等，1998；Baker 和 Coyle，2009），FGDC（Di 等，2000），或 ISO/TC211（Di，2003）等，主要描述特定的单一数据项或服务。GeoWeb 的可搜索元数据与之根本不同，它为物理或概念对象提供语义和地理描述，这些对象可能具有多种不同的表示形式。GeoWeb 模仿了互联网的域名管理机制，并采用等经度和纬度的网格划分方法构建空间信息管理与发布系统。它是域名与地理信息映射的实现模式，是一个可扩展的开放式全球网络地理索引。然而，GeoWeb 仅允许用户根据指定的经纬度访问三层网格的域名，缺乏直观性。例如，当用户希望访问某个行政区域的数据时，GeoWeb 的访问实现较为困难。GeoWeb 缺乏统一的空间数据识别模型，仅逻辑上组织同一地理范围内的数据，因此无法解决因识别方式不同导致的多源空间数据交换与共享问题。
What3words is an addressing and location reference system that uses randomly generated short-chain strings as identifiers to define the location of any 3mxx3m3 \mathrm{~m} \times 3 \mathrm{~m} grid on the Earth (Jiang and Stefanakis, 2018b). The addressing system can significantly improve the customer experience because imprecise latitude and longitude coordinates can lead to data ambiguity (Stefanakis, 2016). What3words improves the readability of grid coding by converting imperceptible numbers into familiar word combinations, making it easier for people to remember and more user-friendly (Jiang, 2018). In terms of word selection, What3words includes an error-checking mechanism in which words with similar pronunciations are assigned to different grid units located far apart in space (Jiang and Stefanakis, 2018b). What3words provides applications such as websites, IOS, Android, and API interfaces. Users can achieve bidirectional conversion between the three-word addresses corresponding to the grid unit and the latitude and longitude coordinates (Day and Macgregor, 2020). In 2016, the Mongolian government announced the use of What3words as the national addressing system (what3words Limited, 2016). Jiang and Stefanakis proposed a five-word extension identifier for What3words (Jiang and Stefanakis, 2018a). What3Word employs global discrete grids to address challenges in location identification, spatial information management, and publishing. It can be converted to real coordinates, and compared with street addresses, postal codes, longitude and latitude, and mobile short links, the three words address is easy to remember. A location coding system, designed for quick, convenient, and unambiguous retrieval of accurate locations, was developed. However, What3Words has a fixed resolution, and grid labels do not imply spatial relationships. What3Words, like GeoWeb, integrates multi-source data through platform construction but does not solve the problem of unified data identification. What3words 是一种基于随机生成的短字符串作为标识符的地址和位置参考系统，用于定义地球上任何 3mxx3m3 \mathrm{~m} \times 3 \mathrm{~m} 网格的位置（江和斯蒂法纳基斯，2018b）。该地址系统可显著提升用户体验，因为不精确的经纬度坐标可能导致数据模糊（斯蒂法纳基斯，2016）。What3words 通过将难以察觉的数字转换为熟悉的词组，提升了网格编码的可读性，使人们更容易记忆且更用户友好（Jiang，2018）。在词汇选择方面，What3words 包含一个错误检查机制，其中发音相似的词会被分配到空间上相距较远的不同网格单元（Jiang 和 Stefanakis，2018b）。What3words 提供网站、iOS、Android 和 API 接口等应用程序。用户可实现网格单元对应的三词地址与经纬度坐标之间的双向转换（Day 和 Macgregor，2020）。2016 年，蒙古国政府宣布采用 What3words 作为国家地址系统（what3words Limited，2016）。江和斯蒂法纳基斯提出了 What3words 的五词扩展标识符（Jiang and Stefanakis，2018a）。What3Word 采用全球离散网格来解决位置识别、空间信息管理和发布中的挑战。它可以转换为真实坐标，并与街道地址、邮政编码、经纬度以及移动短链接进行比较，三词地址易于记忆。一种位置编码系统被开发出来，旨在实现快速、便捷且无歧义地检索准确位置。 然而，What3Words 具有固定的分辨率，且网格标签并不表示空间关系。与 GeoWeb 类似，What3Words 通过平台构建整合多源数据，但并未解决统一数据识别的难题。
Traditional geographic domain name methods, including positional semantic conversion, information cataloging, and industrial standards, aim to standardize location identification. However, they often lead to disordered data storage and low matching efficiency. GeoWeb offers a distributed metadata framework for accessing geo-referenced data, although it lacks intuitive access and a unified spatial identification model. What3words enhances location identification by using memorable word combinations for specific grid areas, thereby improving usability, though it faces limitations related to fixed resolution. These methods represent advancements in ULI management but struggle with unified identification and multi-source data sharing. To address the needs of a unified organization of ULI and precise cognition of spatial locations between humans and machines, the GGRN facilitates spatial 传统地理域名方法，包括位置语义转换、信息分类和行业标准，旨在标准化位置识别。然而，这些方法常常导致数据存储混乱和匹配效率低下。GeoWeb 提供了一个分布式元数据框架，用于访问地理参考数据，尽管它缺乏直观的访问方式和统一的空间识别模型。What3words 通过为特定网格区域使用易于记忆的词组来增强位置识别，从而提升了可用性，但其面临与固定分辨率相关的限制。这些方法代表了 ULI 管理领域的进步，但在统一识别和多源数据共享方面仍存在挑战。为满足 ULI 的统一组织需求以及人类与机器之间对空间位置的精准认知，GGRN 促进了空间
location identification, enabling precise cognition for both humans and machines, as well as ULI organization and management based on the GGRN. This paper discusses the GGRN’s logical structure and spatial hierarchy, the methods for GGRN code generation, and the organization of ULI based on the GGRN. 位置识别，实现人类与机器的精准认知，以及基于 GGRN 的 ULI 组织与管理。本文探讨了 GGRN 的逻辑结构与空间层次，GGRN 代码生成方法，以及基于 GGRN 的 ULI 组织架构。
2. Methods 2. 方法
2.1. Related concepts 2.1. 相关概念
2.1.1. GGRN
The domain name is the name of a computer or computer group on the Internet, composed of a string used to identify the electronic location during data transmission. The name of a geospatial region refers to the name of every region on Earth. The GGRN is the name of each grid region on Earth. The GGRN uses the DGGS to directly associate each data or dataset with location information for a specific area on Earth and can achieve a unified expression of the organizational framework for multisource heterogeneous geospatial data. GGRN is similar to the domain names on the Internet. The top-level GGRN were decomposed into subGGRNs. The GGRN gives unique grid region names to all types of data, ranging from the global scale to the centimeter level. The GGRN solves the common precise cognition of humans and computers on spatial grid addresses. The GGRN can carry out geographical recognition, retrieval, and location association on the ULI according to regional names, thereby enhancing geospatial data. 域名是互联网中计算机或计算机组的名称，由一串用于在数据传输过程中识别电子位置的字符串组成。地理空间区域的名称指地球上每个区域的名称。GGRN 是地球上每个网格区域的名称。GGRN 利用 DGGS 直接将每个数据或数据集与地球上特定区域的位置信息关联，并能实现多源异构地理空间数据组织框架的统一表达。GGRN 与互联网上的域名类似。顶级 GGRN 被分解为子 GGRN。GGRN 为所有类型的数据赋予唯一的网格区域名称，范围从全球尺度到厘米级别。GGRN 解决了人类与计算机在空间网格地址上的精准认知问题。GGRN 可根据区域名称在统一位置标识符（ULI）上进行地理识别、检索及位置关联，从而提升地理空间数据的价值。
2.1.2. GGRN code 2.1.2. GGRN 代码
The GGC is the gridded code identification of the Earth’s spatial position and spatial objects by the DGGS subdivision. GGC encodes the Earth’s 2D or 3D space and reduces it to a one-dimensional space, forming a concise and readable grid code. Compared to purely logical identifiers with no specific meaning, GGC has a clear geographical meaning and features such as multiscale, localization, computational, and indexing. The GGRN code is the GGC or set of GGCs corresponding to the spatial area described by the GGRN, which is the resolution result of the GGRN. GGC 是 DGGS 分区对地球空间位置和空间对象的网格化代码标识。GGC 对地球的 2D 或 3D 空间进行编码并将其简化为一维空间，形成简洁易读的网格代码。与仅具有逻辑含义的纯逻辑标识符相比，GGC 具有明确的地理意义，并具备多尺度、定位、计算和索引等特征。GGRN 代码是与 GGRN 描述的空间区域对应的 GGC 或 GGC 集合，它是 GGRN 的分辨率结果。
2.2. GGRN logical structure and spatial hierarchy 2.2. GGRN 的逻辑结构与空间层次结构
2.2.1. GGRN Composition and logical structure 2.2.1. GGRN 组成与逻辑结构
The GGRN consists of personal segments, area segments, organization segments, root segments, and ULI target codes and is classified by English half-width periods, as shown in Fig. 1A. The position of the RRN in the GGRN was similar to that of the top-level domain name in the DNS. In this paper, RRN is denoted as “.geosot”. The organization segment refers to the type of organization corresponding to different industries. The area segment refers to the identification of administrative divisions that express the geographical and spatial scope. We divided the area into five levels based on administrative divisions: country (cou), provincial (pro), city (cit), district (dis), and street (str). The entire area segment is represented sequentially by different levels of area segments, separated by half width periods, in the format of: street name >> district name >> city name >> province name >> country name. The personal segment refers to users who are granted permission to define their own identification for a grid within a spatial scope expressed by an ARN and to ensure local uniqueness within the spatial scope expressed by the ARN. The ULI target code was used to identify ULI within the spatial scope expressed by the PRN. The GGRN adopts an ORN, ARN, and PRN. ORN is a type identification, whereas ORN and PRN are spatial identifications. The logical relationships between region names at different levels in the GGRN are shown in Fig. 1B. The RRN governs multiple ORNs, each ORN governs multiple ARNs, each ARN governs multiple PRNs, and each PRN contains multiple ULI target codes, thus providing effective support for the multilevel organizational management of ULI. GGRN 由个人段、区域段、组织段、根段和 ULI 目标代码组成，并通过英文半角句点进行分类，如图 1A 所示。GGRN 中 RRN 的位置与 DNS 中顶级域名的位置相似。本文中，RRN 表示为“.geosot”。组织段指对应不同行业的组织类型。区域段用于标识表达地理和空间范围的行政区划。我们根据行政区划将区域分为五个层次：国家（cou）、省（pro）、市（cit）、区（dis）和街道（str）。整个区域段通过不同级别的区域段按顺序表示，各段之间用半宽句点分隔，格式为：街道名称 >> 区名称 >> 市名称 >> 省名称 >> 国家名称。个人段指的是被授予权限在由 ARN 表示的空间范围内定义自己的标识，并在由 ARN 表示的空间范围内确保本地唯一性的用户。ULI 目标代码用于在由 PRN 表示的空间范围内识别 ULI。GGRN 采用 ORN、ARN 和 PRN。ORN 是类型标识，而 ORN 和 PRN 是空间标识。GGRN 中不同层次区域名称之间的逻辑关系如图 1B 所示。RRN 管理多个 ORN，每个 ORN 管理多个 ARN，每个 ARN 管理多个 PRN，每个 PRN 包含多个 ULI 目标代码，从而为 ULI 的多层次组织管理提供了有效支持。
Fig. 2. GGRN reference framework. 图 2. GGRN 参考框架。
The GGRN is grafted onto the existing DNS (Lyu et al., 2022); therefore, it is necessary to follow the naming conventions of the DNS. Internationalized domain names (Klensin, 2010) in DNS refer to internet domain names that are partially or entirely composed of special characters or letters, such as Chinese, Arabic, Tamil, and Slavic. Internationalized domain names were written using Punycode (Costello, 2003) and stored in the DNS as a string using the American Standard Code for Information Interchange (Cerf, 1969). GGRN 接枝到现有的 DNS（Lyu 等，2022）；因此，必须遵循 DNS 的命名规范。DNS 中的国际化域名（Klensin，2010）指的是部分或全部由特殊字符或字母组成的互联网域名，例如中文、阿拉伯文、泰米尔文和斯拉夫文。国际化域名使用 Punycode（Costello，2003）编码，并以字符串形式存储在 DNS 中，采用美国信息交换标准代码（Cerf，1969）。
2.2.2. GGRN reference framework and spatial hierarchy 2.2.2. GGRN 参考框架与空间层次结构
The spatial hierarchy of the GGRN can be divided into a 2D spatial hierarchy and a 3D spatial hierarchy, as shown in Fig. 1C. Specifically, GGRN 的空间层次结构可分为二维空间层次结构和三维空间层次结构，如图 1C 所示。具体而言，
(1) The 2D spatial hierarchy of the GGRN is oriented towards the ARN, and the geographical coordinate-subdividing grid with one dimensional integer coding on a 2^(n)2^{\mathrm{n}}-tree (GeoSOT) (Cheng et al., 2012; Cheng et al., 2016) serves as the reference framework, as shown in Fig. 2a. Based on the quadtree grid subdivision method, different grid units are divided, and the set of grid units uses the corresponding ARN for spatial identification. (1) GGRN 的二维空间层次结构面向 ARN，采用基于 2^(n)2^{\mathrm{n}} 树的一维整数编码地理坐标划分网格（GeoSOT）（Cheng et al., 2012；Cheng et al., 2016）作为参考框架，如图 2a 所示。基于四叉树网格划分方法，将网格划分为不同单元，网格单元集通过对应的 ARN 进行空间标识。
(2) The 3D spatial hierarchy of the GGRN is oriented towards the PRN. First, GeoSOT was extended to high dimensions to form (2) GGRN 的 3D 空间层次结构以 PRN 为导向。首先，GeoSOT 被扩展到高维空间以形成
GeoSOT-3D (Hu et al., 2015), as shown in Fig. 2b. Subsequently, grid levels were extracted to form the Beidou 3D grid location code (B3GLC) (China National Standard, 2020) based on GeoSOT-3D. B3GLC covers different accuracies at the meter, decimeter, and centimeter levels, and is compatible with existing major map frames. Finally, a certain grid level is extracted for a specific industry as the industry location code, which serves as the reference framework for the 3D spatial hierarchy of the GGRN. The octree grid subdivision method divides data into different grid units, and each grid unit uses its corresponding PRN for spatial identification. GeoSOT-3D（胡等，2015），如图 2b 所示。随后，基于 GeoSOT-3D 提取网格层，形成北斗 3D 网格位置码（B3GLC）（中国国家标准，2020）。B3GLC 涵盖米级、分米级和厘米级不同精度，并与现有主要地图框架兼容。最终，为特定行业提取特定网格级别作为行业位置代码，作为 GGRN 三维空间层次结构的参考框架。八叉树网格划分方法将数据划分为不同网格单元，每个网格单元使用对应的 PRN 进行空间识别。
The mathematical definition of GGRN spatial hierarchy can be expressed as: GGRN 空间层次结构的数学定义可表示为： {E,G(x),R(x),T(x)}\{E, G(x), R(x), T(x)\}
where xx is the spatial hierarchical structure category of the GGRN, taking on values {2,3}\{2,3\} to denote 2D and 3D, respectively; EE is Earth, symbolizing Earth’s space; G(x)G(x) is Grid, signifying the sub-grids resulting from the subdivision of Earth’s space; and R(x)R(x) is Region Name, representing the GGRN expression. 其中， xx 表示 GGRN 的空间分层结构类别，取值为 {2,3}\{2,3\} ，分别表示 2D 和 3D； EE 表示地球，象征地球空间； G(x)G(x) 表示网格，表示地球空间划分后形成的子网格； R(x)R(x) 表示区域名称，表示 GGRN 的表达。
Employing this subdivision approach yields a sequential, multilevel 采用这种细分方法可以得到一个顺序的、多层次的
Based on the size of the vector layer area of the administrative division AA, first select a coarser region name space subdivision level SS, obtain its corresponding GeoSOT grid set G=G={G_(i)∣G_(0),G_(1),G_(3),dots,G_(n)}\left\{G_{i} \mid G_{0}, G_{1}, G_{3}, \ldots, G_{n}\right\}. Initialize the final grid subdivision set G_("final ")=G_{\text {final }}=O/\varnothing and intermediate storage set G_("temp ")=O/G_{\text {temp }}=\varnothing. And S_(A)S_{A} is the maximum subdivision level corresponding to AA. 根据行政区划的矢量图层面积大小 AA ，首先选择一个较粗的区域名称空间划分级别 SS ，获取其对应的 GeoSOT 网格集 G=G={G_(i)∣G_(0),G_(1),G_(3),dots,G_(n)}\left\{G_{i} \mid G_{0}, G_{1}, G_{3}, \ldots, G_{n}\right\} 。初始化最终网格划分集 G_("final ")=G_{\text {final }}=O/\varnothing 和中间存储集 G_("temp ")=O/G_{\text {temp }}=\varnothing 。其中， S_(A)S_{A} 是与 AA 对应的最大划分级别。
Step 2.1 Calculate the proportion of the vector layer area of AA in G_(i)G_{i}, overlap(A).
Step 2.2 If overlap(A)=0\operatorname{overlap}(A)=0, skip Step 2.3 and Step 2.4.
Step 2.3 If overlap(A) > 0.95,G_("final ")=G_("final ")uuG_(i)\operatorname{overlap}(A)>0.95, G_{\text {final }}=G_{\text {final }} \cup G_{i} and skip Step 2.4. Step 2.4 Calculate the next level grid of the subdivision level S_(G_(i))S_{G_{i}} corresponding to G_(i),G_(i)^(')((S_(G_(i))+1):}G_{i}, G_{i}^{\prime}\left(\left(S_{G_{i}}+1\right)\right. level grid), and G_("temp ")=G_("temp ")uuG_(i)^(')G_{\text {temp }}=G_{\text {temp }} \cup G_{i}^{\prime}.
Traverse grid set G :
Step 2.1 Calculate the proportion of the vector layer area of A in G_(i), overlap(A).
Step 2.2 If overlap(A)=0, skip Step 2.3 and Step 2.4.
Step 2.3 If overlap(A) > 0.95,G_("final ")=G_("final ")uuG_(i) and skip Step 2.4. Step 2.4 Calculate the next level grid of the subdivision level S_(G_(i)) corresponding to G_(i),G_(i)^(')((S_(G_(i))+1):} level grid), and G_("temp ")=G_("temp ")uuG_(i)^(').| Traverse grid set $G$ : |
| :--- |
| Step 2.1 Calculate the proportion of the vector layer area of $A$ in $G_{i}$, overlap(A). |
| Step 2.2 If $\operatorname{overlap}(A)=0$, skip Step 2.3 and Step 2.4. |
| Step 2.3 If $\operatorname{overlap}(A)>0.95, G_{\text {final }}=G_{\text {final }} \cup G_{i}$ and skip Step 2.4. Step 2.4 Calculate the next level grid of the subdivision level $S_{G_{i}}$ corresponding to $G_{i}, G_{i}^{\prime}\left(\left(S_{G_{i}}+1\right)\right.$ level grid), and $G_{\text {temp }}=G_{\text {temp }} \cup G_{i}^{\prime}$. |
Repeat Step 2 and Step 3 until S > S_(A)-1S>S_{A}-1 or G=O/G=\varnothing. 重复步骤 2 和步骤 3，直到出现 S > S_(A)-1S>S_{A}-1 或 G=O/G=\varnothing 。
Step 5 步骤 5
G_("final ")=G_("final ")uu GG_{\text {final }}=G_{\text {final }} \cup G.
Step 6 步骤 6
Output G_("final ")G_{\text {final }}, as the final grid subdivision set of AA, is the grid set corresponding to SARN. 输出 G_("final ")G_{\text {final }} ，作为 AA 的最终网格划分集，是与 SARN 对应的网格集。
Order number Algorithm steps
Step 1 Based on the size of the vector layer area of the administrative division A, first select a coarser region name space subdivision level S, obtain its corresponding GeoSOT grid set G= {G_(i)∣G_(0),G_(1),G_(3),dots,G_(n)}. Initialize the final grid subdivision set G_("final ")= O/ and intermediate storage set G_("temp ")=O/. And S_(A) is the maximum subdivision level corresponding to A.
Step 2 "Traverse grid set G :
Step 2.1 Calculate the proportion of the vector layer area of A in G_(i), overlap(A).
Step 2.2 If overlap(A)=0, skip Step 2.3 and Step 2.4.
Step 2.3 If overlap(A) > 0.95,G_("final ")=G_("final ")uuG_(i) and skip Step 2.4. Step 2.4 Calculate the next level grid of the subdivision level S_(G_(i)) corresponding to G_(i),G_(i)^(')((S_(G_(i))+1):} level grid), and G_("temp ")=G_("temp ")uuG_(i)^(')."
Step 3 S=S+1(S < 26),G=G_("temp "), and G_("temp ")=O/.
Step 4 Repeat Step 2 and Step 3 until S > S_(A)-1 or G=O/.
Step 5 G_("final ")=G_("final ")uu G.
Step 6 Output G_("final "), as the final grid subdivision set of A, is the grid set corresponding to SARN.| Order number | Algorithm steps |
| :--- | :--- |
| Step 1 | Based on the size of the vector layer area of the administrative division $A$, first select a coarser region name space subdivision level $S$, obtain its corresponding GeoSOT grid set $G=$ $\left\{G_{i} \mid G_{0}, G_{1}, G_{3}, \ldots, G_{n}\right\}$. Initialize the final grid subdivision set $G_{\text {final }}=$ $\varnothing$ and intermediate storage set $G_{\text {temp }}=\varnothing$. And $S_{A}$ is the maximum subdivision level corresponding to $A$. |
| Step 2 | Traverse grid set $G$ : <br> Step 2.1 Calculate the proportion of the vector layer area of $A$ in $G_{i}$, overlap(A). <br> Step 2.2 If $\operatorname{overlap}(A)=0$, skip Step 2.3 and Step 2.4. <br> Step 2.3 If $\operatorname{overlap}(A)>0.95, G_{\text {final }}=G_{\text {final }} \cup G_{i}$ and skip Step 2.4. Step 2.4 Calculate the next level grid of the subdivision level $S_{G_{i}}$ corresponding to $G_{i}, G_{i}^{\prime}\left(\left(S_{G_{i}}+1\right)\right.$ level grid), and $G_{\text {temp }}=G_{\text {temp }} \cup G_{i}^{\prime}$. |
| Step 3 | $S=S+1(S<26), G=G_{\text {temp }}$, and $G_{\text {temp }}=\varnothing$. |
| Step 4 | Repeat Step 2 and Step 3 until $S>S_{A}-1$ or $G=\varnothing$. |
| Step 5 | $G_{\text {final }}=G_{\text {final }} \cup G$. |
| Step 6 | Output $G_{\text {final }}$, as the final grid subdivision set of $A$, is the grid set corresponding to SARN. |
Table 2 表 2
Corresponding table of administrative division levels, ARNs, SARNs, and CARNs. 行政区划级别、行政区划编号（ARN）、特殊行政区划编号（SARN）与中央行政区划编号（CARN）对应表。
Administrative division level 行政区划级别
Set of ARNs 一组 ARNs
Set of SARNs SARN 系列
Set of CARNs CARN 系列
cou 库
uuu_(i=0)^(m_("cou "))ARN_(i)\bigcup_{i=0}^{m_{\text {cou }}} A R N_{i}
uuu_(i=0)^(m_("cou "))SARN_(i)^("cou ")\bigcup_{i=0}^{m_{\text {cou }}} S A R N_{i}^{\text {cou }}
uuu_(i=0)^(m_("cou "))uuu_(j=0)^(n_(i)^("cou "))CARN_(ij)^("cou ")\bigcup_{i=0}^{m_{\text {cou }}} \bigcup_{j=0}^{n_{i}^{\text {cou }}} C A R N_{i j}^{\text {cou }}
pro 专业
uuu_(i=0)^(m_("pro "))ARN_(i)\bigcup_{i=0}^{m_{\text {pro }}} A R N_{i}
uuu_(i=0)^(m_(pro))SARN_(i)^(pro)\bigcup_{i=0}^{m_{p r o}} S A R N_{i}^{p r o}
uuu_(i=0)^(m_(pro))uuu_(j=0)^(n_(i)^(pro))CARN_(ij)^(pro)\bigcup_{i=0}^{m_{p r o}} \bigcup_{j=0}^{n_{i}^{p r o}} C A R N_{i j}^{p r o}
cit 引用
uuu_(i=0)^(m_("ct "))ARN_(i)\bigcup_{i=0}^{m_{\text {ct }}} A R N_{i}
uuu_(i=0)^(m_(cit))SARN_(i)^(cit)\bigcup_{i=0}^{m_{c i t}} S A R N_{i}^{c i t}
uuu_(i=0)^(m_(cit))uuu_(j=0)^(n_(i)^(cit))CARN_(ij)^(cit)\bigcup_{i=0}^{m_{c i t}} \bigcup_{j=0}^{n_{i}^{c i t}} C A R N_{i j}^{c i t}
dis 取消
uuu_(i=0)^(m_("dis "))ARN_(i)\bigcup_{i=0}^{m_{\text {dis }}} A R N_{i}
uuu_(i=0)^(m_(dis))uuu_(j=0)^(n_(i)^(dis))CARN_(ij)^(dis)\bigcup_{i=0}^{m_{d i s}} \bigcup_{j=0}^{n_{i}^{d i s}} C A R N_{i j}^{d i s}
str
uuu_(i=0)^(m_("stf "))ARN_(i)\bigcup_{i=0}^{m_{\text {stf }}} A R N_{i}
uuu_(i=0)^(m_("str "))SARN_(i)^("str ")\bigcup_{i=0}^{m_{\text {str }}} S A R N_{i}^{\text {str }}
uuu_(i=0)^(m_(str))uuu_(j=0)^(n_(i)^(str))CARN_(ij)^(str)\bigcup_{i=0}^{m_{s t r}} \bigcup_{j=0}^{n_{i}^{s t r}} C A R N_{i j}^{s t r}
Administrative division level Set of ARNs Set of SARNs Set of CARNs
cou uuu_(i=0)^(m_("cou "))ARN_(i) uuu_(i=0)^(m_("cou "))SARN_(i)^("cou ") uuu_(i=0)^(m_("cou "))uuu_(j=0)^(n_(i)^("cou "))CARN_(ij)^("cou ")
pro uuu_(i=0)^(m_("pro "))ARN_(i) uuu_(i=0)^(m_(pro))SARN_(i)^(pro) uuu_(i=0)^(m_(pro))uuu_(j=0)^(n_(i)^(pro))CARN_(ij)^(pro)
cit uuu_(i=0)^(m_("ct "))ARN_(i) uuu_(i=0)^(m_(cit))SARN_(i)^(cit) uuu_(i=0)^(m_(cit))uuu_(j=0)^(n_(i)^(cit))CARN_(ij)^(cit)
dis uuu_(i=0)^(m_("dis "))ARN_(i) uuu_(i=0)^(m_("dis ")) SARN _(i)^("dis ") uuu_(i=0)^(m_(dis))uuu_(j=0)^(n_(i)^(dis))CARN_(ij)^(dis)
str uuu_(i=0)^(m_("stf "))ARN_(i) uuu_(i=0)^(m_("str "))SARN_(i)^("str ") uuu_(i=0)^(m_(str))uuu_(j=0)^(n_(i)^(str))CARN_(ij)^(str)| Administrative division level | Set of ARNs | Set of SARNs | Set of CARNs |
| :--- | :--- | :--- | :--- |
| cou | $\bigcup_{i=0}^{m_{\text {cou }}} A R N_{i}$ | $\bigcup_{i=0}^{m_{\text {cou }}} S A R N_{i}^{\text {cou }}$ | $\bigcup_{i=0}^{m_{\text {cou }}} \bigcup_{j=0}^{n_{i}^{\text {cou }}} C A R N_{i j}^{\text {cou }}$ |
| pro | $\bigcup_{i=0}^{m_{\text {pro }}} A R N_{i}$ | $\bigcup_{i=0}^{m_{p r o}} S A R N_{i}^{p r o}$ | $\bigcup_{i=0}^{m_{p r o}} \bigcup_{j=0}^{n_{i}^{p r o}} C A R N_{i j}^{p r o}$ |
| cit | $\bigcup_{i=0}^{m_{\text {ct }}} A R N_{i}$ | $\bigcup_{i=0}^{m_{c i t}} S A R N_{i}^{c i t}$ | $\bigcup_{i=0}^{m_{c i t}} \bigcup_{j=0}^{n_{i}^{c i t}} C A R N_{i j}^{c i t}$ |
| dis | $\bigcup_{i=0}^{m_{\text {dis }}} A R N_{i}$ | $\bigcup_{i=0}^{m_{\text {dis }}}$ SARN ${ }_{i}^{\text {dis }}$ | $\bigcup_{i=0}^{m_{d i s}} \bigcup_{j=0}^{n_{i}^{d i s}} C A R N_{i j}^{d i s}$ |
| str | $\bigcup_{i=0}^{m_{\text {stf }}} A R N_{i}$ | $\bigcup_{i=0}^{m_{\text {str }}} S A R N_{i}^{\text {str }}$ | $\bigcup_{i=0}^{m_{s t r}} \bigcup_{j=0}^{n_{i}^{s t r}} C A R N_{i j}^{s t r}$ |
set of subgrids denoted as G(x)_(0),G(x)_(1),G(x)_(2),dots,G(x)_(n)G(x)_{0}, G(x)_{1}, G(x)_{2}, \ldots, G(x)_{n}. 表示为 G(x)_(0),G(x)_(1),G(x)_(2),dots,G(x)_(n)G(x)_{0}, G(x)_{1}, G(x)_{2}, \ldots, G(x)_{n} 的子网格集合。 G(x)_(i)={[2DGrid","x=2],[3DGrid","x=3],i in[0,32]:}G(x)_{i}=\left\{\begin{array}{l}2 D G r i d, x=2 \\ 3 D G r i d, x=3\end{array}, i \in[0,32]\right.
In addition, T(x)T(x) is tree, denotes the grid subdivision tree method adopted by the GGRN Reference Framework. 此外， T(x)T(x) 表示树，用于表示 GGRN 参考框架中采用的网格划分树方法。 T(x)={[" Quad "-" tree "","x=2],[" Oc "-" tree "","x=3]:}T(x)=\left\{\begin{array}{c}\text { Quad }- \text { tree }, x=2 \\ \text { Oc }- \text { tree }, x=3\end{array}\right.
ARN Space (SARN) refers to a grid-based spatial expression of administrative divisions. The ARN code (CARN) is a multilevel gridded coding set identification for SARN. Each ARN corresponds to a SARN, and each SARN corresponds to an ARN code. Therefore, a mapping ARN 空间（SARN）是指基于网格的行政区划空间表达。ARN 代码（CARN）是用于识别 SARN 的多级网格编码集。每个 ARN 对应一个 SARN，每个 SARN 对应一个 ARN 代码。因此，存在一个映射关系。
Determine the spatial area Area_(u)A r e a_{u} and expression scale Sca_(u)S c a_{u} required by industry users. 确定行业用户所需的空间范围 Area_(u)A r e a_{u} 和表达尺度 Sca_(u)S c a_{u} 。
Step 2 步骤 2
Compare Sca_(u)S c a_{u} with the spatial scales {S_(0),S_(1),S_(2),dots,S_(9)}\left\{S_{0}, S_{1}, S_{2}, \ldots, S_{9}\right\} corresponding to different subdivision levels {L_(0),L_(1),L_(2),dots,L_(9)}\left\{L_{0}, L_{1}, L_{2}, \ldots, L_{9}\right\} in B3GLC. Through this comparison, determine the subdivision level L_(i)L_{i} associated with the grid scale S_(i)S_{i} that is closest to Sca_(u)S c a_{u}. 将 Sca_(u)S c a_{u} 与 B3GLC 中不同细分级别 {L_(0),L_(1),L_(2),dots,L_(9)}\left\{L_{0}, L_{1}, L_{2}, \ldots, L_{9}\right\} 对应的空间尺度 {S_(0),S_(1),S_(2),dots,S_(9)}\left\{S_{0}, S_{1}, S_{2}, \ldots, S_{9}\right\} 进行比较。通过此比较，确定与网格尺度 S_(i)S_{i} 最接近的细分级别 L_(i)L_{i} 。
Step 3 步骤 3
According to the subdivision level L_(i)L_{i} of B3GLC, perform an Oc-tree grid subdivision on Area _(u)_{u}. 根据 B3GLC 的细分级别 L_(i)L_{i} ，对区域 _(u)_{u} 进行 Oc-树网格细分。
Step 4 步骤 4
Output the grid subdivision results, i.e., the subdivision grid set GSet _(u)_{u} that represents ULI within Area _(u)_{u}. This set corresponds to the SPRN set SPRN_Set _(u){ }_{u}. 输出网格划分结果，即表示区域 _(u)_{u} 内 ULI 的划分网格集 GSet _(u)_{u} 。该集对应于 SPRN 集 SPRN_Set _(u){ }_{u} 。
Order number Algorithm steps
Step 1 Determine the spatial area Area_(u) and expression scale Sca_(u) required by industry users.
Step 2 Compare Sca_(u) with the spatial scales {S_(0),S_(1),S_(2),dots,S_(9)} corresponding to different subdivision levels {L_(0),L_(1),L_(2),dots,L_(9)} in B3GLC. Through this comparison, determine the subdivision level L_(i) associated with the grid scale S_(i) that is closest to Sca_(u).
Step 3 According to the subdivision level L_(i) of B3GLC, perform an Oc-tree grid subdivision on Area _(u).
Step 4 Output the grid subdivision results, i.e., the subdivision grid set GSet _(u) that represents ULI within Area _(u). This set corresponds to the SPRN set SPRN_Set _(u).| Order number | Algorithm steps |
| :--- | :--- |
| Step 1 | Determine the spatial area $A r e a_{u}$ and expression scale $S c a_{u}$ required by industry users. |
| Step 2 | Compare $S c a_{u}$ with the spatial scales $\left\{S_{0}, S_{1}, S_{2}, \ldots, S_{9}\right\}$ corresponding to different subdivision levels $\left\{L_{0}, L_{1}, L_{2}, \ldots, L_{9}\right\}$ in B3GLC. Through this comparison, determine the subdivision level $L_{i}$ associated with the grid scale $S_{i}$ that is closest to $S c a_{u}$. |
| Step 3 | According to the subdivision level $L_{i}$ of B3GLC, perform an Oc-tree grid subdivision on Area $_{u}$. |
| Step 4 | Output the grid subdivision results, i.e., the subdivision grid set GSet $_{u}$ that represents ULI within Area $_{u}$. This set corresponds to the SPRN set SPRN_Set ${ }_{u}$. |
ARN_Set _(j)^(ORN_(i)),jin{{ }_{j}^{O R N_{i}}, \mathrm{j} \in\{ cou, pro, cit, dis, str }\} ARN_Set _(j)^(ORN_(i)),jin{{ }_{j}^{O R N_{i}}, \mathrm{j} \in\{ 编码, 蛋白质, 细胞, 组织, 结构 }\}
where ORN_(i)O R N_{i} denotes the ii-th ORN. For example, “.Beijing” is an element in the set of provincial-level ARN ARN_Set pro ^(ORN_(i)){ }^{O R N_{i}}, corresponding to SARN. 其中 ORN_(i)O R N_{i} 表示第 ii 个 ORN。例如，“.Beijing” 是省级 ARN 集合 ARN_Set pro ^(ORN_(i)){ }^{O R N_{i}} 中的一个元素，对应于 SARN。
Table 1 shows the multiscale subdivision algorithm for generating the SARN for administrative division AA at a certain level. 表 1 展示了用于生成某一行政区划级别 SARN 的多尺度划分算法。
Each SARN is expressed by a grid set of different levels, indicating that the CARN is a multilevel grid code set. The corresponding table of administrative division levels, ARNs, SARNs, and CARNs, are shown in Table 2, where m={m_("cou "),m_("pro "),m_("cit "),m_("dis "),m_("str ")}m=\left\{m_{\text {cou }}, m_{\text {pro }}, m_{\text {cit }}, m_{\text {dis }}, m_{\text {str }}\right\} represents the number of ARNs corresponding to different administrative division levels, and n_(i)=n_{i}={n_(i)^("cou "),n_(i)^("pro "),n_(i)^("cit "),n_(i)^("dis "),n_(i)^("str ")}\left\{n_{i}^{\text {cou }}, n_{i}^{\text {pro }}, n_{i}^{\text {cit }}, n_{i}^{\text {dis }}, n_{i}^{\text {str }}\right\} represents the number of grid codes in the ii-th SARN at the corresponding administrative division level. 每个 SARN 由不同级别的网格集表示，表明 CARN 是一个多级网格代码集。对应的行政区划级别、ARN、SARN 和 CARN 的对应表如表 2 所示，其中 m={m_("cou "),m_("pro "),m_("cit "),m_("dis "),m_("str ")}m=\left\{m_{\text {cou }}, m_{\text {pro }}, m_{\text {cit }}, m_{\text {dis }}, m_{\text {str }}\right\} 表示不同行政区划级别对应的 ARN 数量， n_(i)=n_{i}={n_(i)^("cou "),n_(i)^("pro "),n_(i)^("cit "),n_(i)^("dis "),n_(i)^("str ")}\left\{n_{i}^{\text {cou }}, n_{i}^{\text {pro }}, n_{i}^{\text {cit }}, n_{i}^{\text {dis }}, n_{i}^{\text {str }}\right\} 表示在对应行政区划级别中第 ii 个 SARN 中的网格代码数量。
The PRN Space (SPRN) is the spatial range corresponding to a subgrid within the 5th level SARN, which corresponds to the grid space position of a certain level of the B3GLC determined by a specific industry. PRN code (CPRN) is a grid location code mapped to the PRN using different industry location codes when targeting different industry types corresponding to different ORNs. Similar to the ARN, there is a mapping relationship between the PRN and CPRN. PRN 空间（SPRN）是 5 级 SARN 中子网格对应的空间范围，该空间范围与特定行业确定的 B3GLC 某一层的网格空间位置相对应。PRN 代码（CPRN）是通过不同行业位置代码映射到 PRN 的网格位置代码，用于针对不同行业类型对应的不同 ORN。与 ARN 类似，PRN 与 CPRN 之间存在映射关系。 PRN harr SPRN harr CPRNP R N \leftrightarrow S P R N \leftrightarrow C P R N
The subdivision algorithm for generating SPRN is shown in Table 3. 用于生成 SPRN 的子网划分算法如表 3 所示。
2.4. ULI management method based on GGRN (UMMG) 2.4. 基于 GGRN 的 ULI 管理方法（UMMG）
2.4.1. Mapping expression of GGRN and GGRN code 2.4.1. GGRN 基因的表达图谱及 GGRN 基因的测序
When we use GGRN to represent the geographic spatial range c in{c_("admin "),c_("person ")∣j in{:}c \in\left\{c_{\text {admin }}, c_{\text {person }} \mid j \in\{\right. cou, pro, cit, dis, str {:}}\left.\}\right\}, there is a mapping relationship ff (GGRN, GGRNcode) between GGRN and GGRN code. The specific formula is as follows: 当我们使用 GGRN 表示地理空间范围 c in{c_("admin "),c_("person ")∣j in{:}c \in\left\{c_{\text {admin }}, c_{\text {person }} \mid j \in\{\right. cou, pro, cit, dis, str {:}}\left.\}\right\} 时，GGRN 与 GGRN 代码之间存在映射关系 ff （GGRN, GGRNcode）。具体公式如下： f(GGRN,GGRNcode)={[GGRN_(o,a_(j)rarrc_(admin)),rarr GCSet_(o,a_(j)rarrc_(admin))","j in{" cou "","" pro, cit, dis, str "}],[,GGRN_(o,a,p rarrc_(str_(k)))rarrG_(o,a,p rarrc_(str_(k)))]:}f(G G R N, G G R N c o d e)=\left\{\begin{array}{cc}G G R N_{o, a_{j} \rightarrow c_{a d m i n}} & \rightarrow G C S e t_{o, a_{j} \rightarrow c_{a d m i n}}, j \in\{\text { cou }, \text { pro, cit, dis, str }\} \\ & G G R N_{o, a, p \rightarrow c_{s t r_{k}}} \rightarrow G_{o, a, p \rightarrow c_{s t r_{k}}}\end{array}\right.
relationship exists between the ARN and the ARN codes. SARN serves as a spatial location middleware that connects the ARN and ARN codes, as described below. ARN 与 ARN 代码之间存在关联关系。SARN 作为空间定位中间件，连接 ARN 与 ARN 代码，具体如下所述。
We simultaneously established a multilevel ARN set that included cou, pro, cit, dis, and str. 我们同时建立了一个多层次的 ARN 集，其中包括 cou、pro、cit、dis 和 str。
where c_("admin ")c_{\text {admin }} is the geographical spatial range corresponding to the jj-th level administrative division, c_(str_(k))c_{s t r_{k}} is the kk-th geographical spatial range within the str level administrative division, oo is the organization segment, aa is the area segment, pp is the personal segment, a_(j)a_{j} is the jj-th level area segment, GGRN_(o,a_(j)rarrc_(admin))G G R N_{o, a_{j} \rightarrow c_{a d m i n}} is the jj-th level ARN, GGRN_(o,a,p rarrc_(str))G G R N_{o, a, p \rightarrow c_{s t r}} is PRN, GCSet _(o,a_(j)rarrc_("admin "))_{o, a_{j} \rightarrow c_{\text {admin }}} is the set of grid codes corresponding to c_("admin ")c_{\text {admin }}, and 其中， c_("admin ")c_{\text {admin }} 表示与第 jj 级行政区划对应的地理空间范围， c_(str_(k))c_{s t r_{k}} 表示在该行政区划内第 kk 级地理空间范围， oo 是组织段， aa 是区域段， pp 是个人段， a_(j)a_{j} 是第 jj -级区域段， GGRN_(o,a_(j)rarrc_(admin))G G R N_{o, a_{j} \rightarrow c_{a d m i n}} 是 jj -级 ARN， GGRN_(o,a,p rarrc_(str))G G R N_{o, a, p \rightarrow c_{s t r}} 是 PRN，GCSet _(o,a_(j)rarrc_("admin "))_{o, a_{j} \rightarrow c_{\text {admin }}} 是与 c_("admin ")c_{\text {admin }} 对应的网格代码集合，并且
Table 4 表 4
Experimental data. 实验数据。
Region name space type 区域名称空间类型
Experimental data 实验数据
Experimental data 实验数据
Experimental data 实验数据
1
2
3
SARN at the str level SARN 在基因表达水平
100,000
100,000
100,000
SPRN
1 million 100 万
5 million 500 万
10 million 1000 万
Region name space type Experimental data Experimental data Experimental data
1 2 3
SARN at the str level 100,000 100,000 100,000
SPRN 1 million 5 million 10 million| Region name space type | Experimental data | Experimental data | Experimental data |
| :--- | :--- | :--- | :--- |
| | 1 | 2 | 3 |
| SARN at the str level | 100,000 | 100,000 | 100,000 |
| SPRN | 1 million | 5 million | 10 million |
G_(o,a,p rarrc_(str_(k)))G_{o, a, p \rightarrow c_{s t r_{k}}} is the grid code corresponding to c_(str_(k))c_{s t r_{k}}, with G_(o,a,p rarrc_(str_(k)))G_{o, a, p \rightarrow c_{s t r_{k}}} 对应的网格代码，其中
GCSet _(o,a_(j)rarrc_("admin "_(j)))={:}_{o, a_{j} \rightarrow c_{\text {admin }_{j}}}=\left\{\right. GridCode _(j)^(1)_{j}^{1}, GridCode _(j)^(2),dots_{j}^{2}, \ldots, GridCode {:_(j)^(n)}\left._{j}^{n}\right\} GCSet _(o,a_(j)rarrc_("admin "_(j)))={:}_{o, a_{j} \rightarrow c_{\text {admin }_{j}}}=\left\{\right. 网格代码 _(j)^(1)_{j}^{1} , 网格代码 _(j)^(2),dots_{j}^{2}, \ldots , 网格代码 {:_(j)^(n)}\left._{j}^{n}\right\}
where nn is the number of subdivision grids corresponding to c_("admin ")c_{\text {admin }}. 其中 nn 表示与 c_("admin ")c_{\text {admin }} 对应的子网格数量。
2.4.2. GGRN indexing mechanism 2.4.2. GGRN 索引机制
This study constructs a ULI Subdivision Index Big Table Based on GGRN (USG). USG registers, manages, and accesses ULI through GGRN and establishes the corresponding physical indexes and storage based on the spatiotemporal subdivision grid architecture as the basic framework. In USG, the primary keys of the GGRN index and GGRN code index coexist and are mapped to each other. Using the GeoSOT spatial code generation operation, the spatial location information of the ULI was transformed into the GeoSOT subdivision code. The ULI is then associated with ORN, ARN, and PRN, which are used as query primary keys (QPK) to obtain the metadata and attribute information of the ULI. Therefore, USG was performed. 本研究基于 GGRN（USG）构建了 ULI 子网格索引大表。USG 通过 GGRN 对 ULI 进行注册、管理和访问，并基于时空子网格划分架构建立相应的物理索引和存储，作为基本框架。在 USG 中，GGRN 索引的主键与 GGRN 代码索引的主键共存并相互映射。通过 GeoSOT 空间代码生成操作，将 ULI 的空间位置信息转换为 GeoSOT 细分代码。随后，ULI 与 ORN、ARN 和 PRN 关联，这些作为查询主键（QPK）用于获取 ULI 的元数据和属性信息。因此，USG 得以实现。
The QPK formula of ARN is as follows. ARN 的 QPK 公式如下。 QPK_(ARN)=uuu_(i=0)^(a)uuu_(1 <= n <= 5)uuu_(j=0)^(b_(n_(i)))(O_:}Q P K_{A R N}=\bigcup_{i=0}^{a} \bigcup_{1 \leq n \leq 5} \bigcup_{j=0}^{b_{n_{i}}}\left(O \_\right.segment i_(i)+i_{i}+ A_segment {:_(j)^(i))\left._{j}^{i}\right) QPK_(ARN)=uuu_(i=0)^(a)uuu_(1 <= n <= 5)uuu_(j=0)^(b_(n_(i)))(O_:}Q P K_{A R N}=\bigcup_{i=0}^{a} \bigcup_{1 \leq n \leq 5} \bigcup_{j=0}^{b_{n_{i}}}\left(O \_\right. 段 i_(i)+i_{i}+ A_段 {:_(j)^(i))\left._{j}^{i}\right)
where aa is the number of types of organization segments in USG, nn is the level of the area segment, O_(-)O_{-}segment _(i)_{i} is the ii-th type organization segment, b_(n_(i))b_{n_{i}} is the number of area segments at the nn-th level under O_(-)O_{-}segment _(i)_{i}, and A_(-)A_{-}segment _(j)^(i)_{j}^{i} is the jj-th area segment under O_(-)O_{-}segment _(i)_{i}. 其中， aa 表示 USG 中组织段的类型数量， nn 表示区域段的级别， O_(-)O_{-} 表示第 _(i)_{i} 级组织段， ii 表示第 b_(n_(i))b_{n_{i}} 级组织段， nn 表示第 O_(-)O_{-} 级区域段， _(i)_{i} 表示第 A_(-)A_{-} 级区域段， _(j)^(i)_{j}^{i} 表示第 jj 级区域段。-th 级别下 O_(-)O_{-} 段 _(i)_{i} 的区域段数量，而 A_(-)A_{-} 段 _(j)^(i)_{j}^{i} 是 O_(-)O_{-} 段 _(i)_{i} 下第 jj -th 区域段。
The QPK formula of PRN is as follows. PRN 的 QPK 公式如下。 QPK_(PRN)=uuu_(i=0)^(a)uuu_(j=0)^(b_(st_(i)))uuu_(k=0)^(c_(i,j))(O_:}Q P K_{P R N}=\bigcup_{i=0}^{a} \bigcup_{j=0}^{b_{s t_{i}}} \bigcup_{k=0}^{c_{i, j}}\left(O \_\right.segment _(i)+A_(_)_{i}+A_{\_}segment _(j)^(i)+P_(_)_{j}^{i}+P_{\_}segment {:_(i,j)^(k))\left._{i, j}^{k}\right) QPK_(PRN)=uuu_(i=0)^(a)uuu_(j=0)^(b_(st_(i)))uuu_(k=0)^(c_(i,j))(O_:}Q P K_{P R N}=\bigcup_{i=0}^{a} \bigcup_{j=0}^{b_{s t_{i}}} \bigcup_{k=0}^{c_{i, j}}\left(O \_\right. 段落 _(i)+A_(_)_{i}+A_{\_} 段落 _(j)^(i)+P_(_)_{j}^{i}+P_{\_} 段落 {:_(i,j)^(k))\left._{i, j}^{k}\right)
where b_(str_(i))b_{s t r_{i}} is the number of area segments at the str level under O_(-)O_{-}segment _(i),c_(i,j)_{i}, \mathrm{c}_{i, j} is the number of personal segments under O_(-)O_{-}segment _(i)_{i} and A_(-)A_{-}segment _(j)^(i){ }_{j}^{i}, and P_(-)P_{-}segment _(i,j)^(k){ }_{i, j}^{k} is the kk-th personal segment under O_(-)O_{-}segment _(i)_{i} and A_(-)A_{-}segment _(j)^(i)_{j}^{i}. 其中， b_(str_(i))b_{s t r_{i}} 表示在 O_(-)O_{-} 段下的区域段数量， _(i),c_(i,j)_{i}, \mathrm{c}_{i, j} 表示在 O_(-)O_{-} 段下的个人段数量， _(i)_{i} 和 A_(-)A_{-} 表示在 _(j)^(i){ }_{j}^{i} 段下的个人段数量， P_(-)P_{-} 表示在 _(i,j)^(k){ }_{i, j}^{k} 段下的个人段数量，而 kk 表示在 O_(-)O_{-} 段下的个人段数量。-th 个人分段，位于 O_(-)O_{-} 分段 _(i)_{i} 和 A_(-)A_{-} 分段 _(j)^(i)_{j}^{i} 之下。
2.4.3. GGRN storage mechanism 2.4.3. GGRN 存储机制
JavaScript Object Notation is a lightweight data exchange format that has good readability and scalability and has great advantages in handling ULI. We store the JavaScript Object Notation file and save the organization segment column, the area segment column, the personal segment column, and their association with ULI ( O_O \_segment _(i),A_(-){ }_{i}, A_{-}segment _(j)^(i){ }_{j}^{i}, P_segment {:t_(i,j)^(k),ULI)\left.t_{i, j}^{k}, U L I\right) to SUG. We obtained the ULI by combining the PRN and ULI target codes. The attribute storage expression formula for SUG is as follows: JavaScript 对象表示法（JavaScript Object Notation，JSON）是一种轻量级的数据交换格式，具有良好的可读性和可扩展性，在处理 ULI 时具有显著优势。我们将 JavaScript 对象表示法文件存储起来，并保存组织段列、区域段列、个人段列及其与 ULI 的关联（ O_O \_ 段 _(i),A_(-){ }_{i}, A_{-} 段 _(j)^(i){ }_{j}^{i} ，P_segment {:t_(i,j)^(k),ULI)\left.t_{i, j}^{k}, U L I\right) ）到 SUG 中。通过结合 PRN 和 ULI 目标代码，我们获得了 ULI。SUG 的属性存储表达式公式如下：
Attribute (QPK)=uuu_(k=0)^(c)(Q P K)=\bigcup_{k=0}^{c} Attribute _(k)^(QPK)(i,n,j,k)=_{k}^{Q P K}(i, n, j, k)= INCLUDE (attribute) 属性 (QPK)=uuu_(k=0)^(c)(Q P K)=\bigcup_{k=0}^{c} 属性 _(k)^(QPK)(i,n,j,k)=_{k}^{Q P K}(i, n, j, k)= 包含 (属性)
where Attribute(QPK) is the attribute information of ULI corresponding to QPK, cc is the number of attribute columns, attribute is the subattribute information of ULI, and INCLUDE() is the defined attribute-containing operation. 其中，Attribute(QPK) 表示与 QPK 对应的 ULI 的属性信息， cc 表示属性列的数量，attribute 表示 ULI 的子属性信息，INCLUDE() 表示已定义的包含属性的操作。
Table 5 表 5
The entry times for experiment data. 实验数据的输入时间。
Experimental data 实验数据
Experimental data 实验数据
Experimental data 实验数据
Experimental data 实验数据
1
2
3
Entry time (s) 入场时间（秒）
52.58
313.41
496.48
Experimental data Experimental data Experimental data Experimental data
1 2 3
Entry time (s) 52.58 313.41 496.48| Experimental data | Experimental data | Experimental data | Experimental data |
| :--- | :--- | :--- | :--- |
| | 1 | 2 | 3 |
| Entry time (s) | 52.58 | 313.41 | 496.48 |
3. Data and environment 3. 数据与环境
UDAC (China National Standard, 2022) is an application extension code of B3GLC in the delivery industry, consisting of the country, delivery company, universal delivery address location (L_UDAC), delivery attributes, and verification codes. L_UDAC represents the 3D spatial location of the delivery address, with a spatial scale of approximately a 1mxx1mxx1m1 \mathrm{~m} \times 1 \mathrm{~m} \times 1 \mathrm{~m} 3D grid (the 8th level grid of B3GLC). We conducted experiments on L_UDAC, which expresses spatial location. UDAC（中国国家标准，2022）是 B3GLC 在物流行业中的应用扩展码，由国家、物流公司、通用配送地址位置（L_UDAC）、配送属性及验证码组成。L_UDAC 表示配送地址的 3D 空间位置，空间尺度约为一个 1mxx1mxx1m1 \mathrm{~m} \times 1 \mathrm{~m} \times 1 \mathrm{~m} 3D 网格（B3GLC 的第 8 级网格）。我们对 L_UDAC 进行了实验，以表达空间位置。
As of the end of 2020, there were 8773 str level administrative divisions in China, corresponding to the str level SARN. Therefore, the experiment simulated 100,000 str level SARN globally based on the approximate proportion of China’s land area to the global land area, and encoded and named them ARN. Simultaneously, the L_UDAC grid subdivision was performed on these SARNs. Then, 1,5 , and 10 million SPRN were randomly selected from these subdivision grids as the simulation experimental data (Table 4). 截至 2020 年底，中国共有 8773 个市级行政区划，对应于市级 SARN。因此，实验基于中国陆地面积占全球陆地面积的近似比例，在全球范围内模拟了 10 万个市级 SARN，并将其编码和命名为 ARN。同时，对这些 SARN 进行了 L_UDAC 网格划分。随后，从这些网格划分中随机选取 150 万、1000 万和 1 亿个 SPRN 作为模拟实验数据（表 4）。
Thus, we established a storage mechanism for GGRN. The GGRN retrieval experiment adopts the < PRN > index, which is a combination index of < personal segment, area segment, organization segment, root segment >>. The experimental industry is the delivery industry, and the organizational segment is the delivery industry. This experiment used the GGRN to retrieve the ULI within the SPRN, returning all the attribute columns of the ULI. The retrieval time is the average of three queries under the same conditions. 因此，我们建立了一个 GGRN 的存储机制。GGRN 检索实验采用< PRN >索引，该索引是< 个人段、区域段、组织段、根段 >> 的组合索引。实验行业为物流行业，组织段为物流行业。本实验使用 GGRN 在 SPRN 中检索 ULI，并返回 ULI 的所有属性列。检索时间为在相同条件下三次查询的平均值。
The experimental development platform used was Microsoft Visual Studio 2017, the programming language was C#, the CPU was an Intel ® Xeon ® Gold 6132 @ 2.60 GHz and 2.59 GHz (two processors), and there was 64 GB of memory. The backend database system was Oracle 11 g and PostgreSQL 9.6 + PostGIS 3.0. 实验开发平台采用的是 Microsoft Visual Studio 2017，编程语言为 C#，CPU 为 Intel® Xeon® Gold 6132 @ 2.60 GHz 和 2.59 GHz（双处理器），内存为 64 GB。后端数据库系统为 Oracle 11g 和 PostgreSQL 9.6 + PostGIS 3.0。
4. Experiment and analysis 4. 实验与分析
The experiment in this study aimed to evaluate the index feasibility and retrieval efficiency of GGRN. This method combines the current mainstream Oracle (Oracle GGRN) and PostgreSQL (PostgreSQL GGRN) databases and compares the retrieval efficiency and database capacity against the corresponding spatial databases, Oracle Spatial and PostgreSQL + PostGIS. The following formula was used to measure the retrieval efficiency improvement ( E_(r)E_{r} ), database capacity consumption (C_(d))\left(C_{d}\right), and comprehensive performance ( P_(c)P_{c} ) of the GGRN: 本研究的实验旨在评估 GGRN 的指标可行性和检索效率。该方法结合了当前主流的 Oracle（Oracle GGRN）和 PostgreSQL（PostgreSQL GGRN）数据库，并与对应的空间数据库 Oracle Spatial 和 PostgreSQL + PostGIS 进行比较，以评估其检索效率和数据库容量。以下公式用于测量 GGRN 的检索效率提升（ E_(r)E_{r} ）、数据库容量消耗（ (C_(d))\left(C_{d}\right) ）及综合性能（ P_(c)P_{c} ）： {[E_(r)=(T_(0)-T_(GGRN))/(T_(0))xx100%],[C_(d)=(S_(0)-S_(GGRN))/(S_(0))xx100%],[P_(c)=(E_(r)+C_(d))/(2)]:}\left\{\begin{array}{c}E_{r}=\frac{T_{0}-T_{G G R N}}{T_{0}} \times 100 \% \\ C_{d}=\frac{S_{0}-S_{G G R N}}{S_{0}} \times 100 \% \\ P_{c}=\frac{E_{r}+C_{d}}{2}\end{array}\right.
where T_(0)T_{0} is the retrieval time of the comparative experiment, T_(GGRN)T_{G G R N} is the retrieval time of GGRN, S_(0)S_{0} is the database capacity consumption of the comparative experiment, and S_(GGRN)S_{G G R N} is the database capacity consumption of GGRN. 其中， T_(0)T_{0} 为比较实验的检索时间， T_(GGRN)T_{G G R N} 为 GGRN 的检索时间， S_(0)S_{0} 为比较实验的数据库容量消耗， S_(GGRN)S_{G G R N} 为 GGRN 的数据库容量消耗。
4.1. Comparative experiment with Oracle spatial 4.1. 与 Oracle 空间的比较实验
Oracles supporting custom data types. Arrays, structures, or classes with constraints can be used to define the object types (Kyte and Kuhn, 支持自定义数据类型的预言机。带约束的数组、结构体或类可用于定义对象类型（Kyte 和 Kuhn，
Table 6 表 6
Index establishment time of Oracle Spatial and Oracle GGRN. Oracle Spatial 和 Oracle GGRN 的索引建立时间。
Experimental data 实验数据
Experimental data 1 实验数据 1
Experimental data 2 实验数据 2
Experimental data 3 实验数据 3
Index establishment time of Oracle Spatial (s) Oracle Spatial 索引建立时间（秒）
167.46
1147.45
2058.87
Index establishment time of Oracle GGRN (s) Oracle GGRN 索引建立时间（秒）
0.59
3.28
5.64
Experimental data Experimental data 1 Experimental data 2 Experimental data 3
Index establishment time of Oracle Spatial (s) 167.46 1147.45 2058.87
Index establishment time of Oracle GGRN (s) 0.59 3.28 5.64| Experimental data | Experimental data 1 | Experimental data 2 | Experimental data 3 |
| :--- | :--- | :--- | :--- |
| Index establishment time of Oracle Spatial (s) | 167.46 | 1147.45 | 2058.87 |
| Index establishment time of Oracle GGRN (s) | 0.59 | 3.28 | 5.64 |
Table 7 表 7
Retrieval times for Oracle Spatial and Oracle GGRN in experimental data 1. Oracle Spatial 和 Oracle GGRN 在实验数据 1 中的检索时间
ID
Retrieval time for Oracle Spatial (ms) Oracle Spatial 的检索时间（毫秒）
Retrieval time for Oracle GGRN (ms) Oracle GGRN 的检索时间（毫秒）
2022). Oracle Spatial is a spatial data management system developed based on this feature of Oracle (2023). Oracle Spatial manages spatial data using metadata tables, spatial data fields (i.e., the MDSYS.SDO_GEOMETRY field in the following text), and spatial indexes. Thus, it provides a series of spatial queries and analytical functions. This paper uses the Oracle data loading tool “sqlloader” to achieve fast data entry through “.ctl” control. The entry times for experimental datasets 1, 2, and 3 are listed in Table 5. 2022). Oracle Spatial 是一款基于 Oracle 这一特性开发的空间数据管理系统（2023）。Oracle Spatial 通过元数据表、空间数据字段（即下文中提到的 MDSYS.SDO_GEOMETRY 字段）以及空间索引来管理空间数据。因此，它提供了一系列空间查询和分析函数。本文使用 Oracle 数据加载工具“sqlloader”通过“ .ctl”控制实现快速数据导入。实验数据集 1、2 和 3 的导入时间如表 5 所示。
4.1.1. Index establishment time 4.1.1. 索引建立时间
The oracle Spatial index establishment mainly includes the MDSYS. SDO_GEOMETRY-type field establishment and the MDSYS. SPATIAL_INDEX-type index establishment. MDSYS. SDO_GEOMETRY can represent points, multipoints, lines, multilines, polygons, multipolygons, bodies, and mixed objects. Based on this, Oracle Spatial implements MDSYS.SPATIAL_INDEX index, also known as the R-tree Oracle 空间索引的建立主要包括 MDSYS. SDO_GEOMETRY 类型字段的建立和 MDSYS. SPATIAL_INDEX 类型索引的建立。MDSYS.SDO_GEOMETRY 字段可表示点、多点、线、多线、多边形、多边形集、实体及混合对象。基于此，Oracle Spatial 实现了 MDSYS.SPATIAL_INDEX 索引，即 R-树索引。
spatial index. The index establishment times for experimental datasets 1, 2, and 3 using Oracle Spatial and Oracle GGRN are listed in Table 6. The index establishment times of both Oracle Spatial and Oracle GGRN increased with an increase in spatial data volume. However, we found that the index establishment time of Oracle GGRN was significantly shorter than that of Oracle Spatial because the MDSYS.SDO_GEOMETRY field establishment and MDSYS.SPATIAL_INDEX index establishment of Oracle Spatial require a significant amount of time to perform calculations. 空间索引。使用 Oracle Spatial 和 Oracle GGRN 对实验数据集 1、2 和 3 建立索引所需的时间如表 6 所示。Oracle Spatial 和 Oracle GGRN 的索引建立时间均随空间数据量增加而增加。然而，我们发现 Oracle GGRN 的索引建立时间显著短于 Oracle Spatial，这是因为 Oracle Spatial 的 MDSYS.SDO_GEOMETRY 字段建立和 MDSYS.SPATIAL_INDEX 索引建立需要大量时间进行计算。
4.1.2. Spatial retrieval time 4.1.2. 空间检索时间
Oracle Spatial and Oracle GGRN randomly selected ten SPRNs from experiment data 1,2 , and 3 for spatial retrieval experiments. The retrieval time was the average of three queries under the same conditions. The Oracle Spatial and GGRN retrieval times for experimental dataset 1 are listed in Table 7, and the average retrieval times for the ten SPRNs are shown in Fig. 3. Oracle Spatial 和 Oracle GGRN 从实验数据 1、2 和 3 中随机选取了 10 个 SPRNs 用于空间检索实验。检索时间为在相同条件下三次查询的平均值。Oracle Spatial 和 GGRN 在实验数据集 1 中的检索时间如表 7 所示，10 个 SPRNs 的平均检索时间如图 3 所示。
The Oracle Spatial and GGRN retrieval times for experimental dataset 2 are listed in Table 8, and the average retrieval times for the ten SPRNs are shown in Fig. 4. Oracle Spatial 和 GGRN 对于实验数据集 2 的检索时间如表 8 所示，而 10 个 SPRN 的平均检索时间如图 4 所示。
The Oracle Spatial and GGRN retrieval times for experimental dataset 3 are listed in Table 9, and the average retrieval times for the ten SPRNs are shown in Fig. 5. Oracle Spatial 和 GGRN 对于实验数据集 3 的检索时间如表 9 所示，而 10 个 SPRN 的平均检索时间如图 5 所示。
Table 10 demonstrates that Oracle GGRN improved the retrieval efficiency of experimental datasets 1,2 , and 3 by 28.00%,50.16%28.00 \%, 50.16 \%, and 39.91 %, respectively, resulting in an average improvement of 39.36 % compared with Oracle Spatial. This indicates that Oracle GGRN has 表 10 表明，Oracle GGRN 分别将实验数据集 1、2 和 3 的检索效率提高了 28.00%,50.16%28.00 \%, 50.16 \% 、和 39.91%，与 Oracle Spatial 相比，平均提升了 39.36%。这表明 Oracle GGRN 具有
Table 8 表 8
Retrieval times for Oracle Spatial and Oracle GGRN in experimental data 2. Oracle Spatial 和 Oracle GGRN 在实验数据 2 中的检索时间。
ID
Retrieval time for Oracle Spatial (ms) Oracle Spatial 的检索时间（毫秒）
Retrieval time for Oracle GGRN (ms) Oracle GGRN 的检索时间（毫秒）
significant advantages over Oracle Spatial when retrieving various volumes of spatial data. This is attributed to the GGRN data organization method, which converts the spatial relationship calculations in traditional spatial queries into field queries, thereby reducing the complexity 在检索各种规模的空间数据时，GGRN 相比 Oracle Spatial 具有显著优势。这得益于 GGRN 的数据组织方法，该方法将传统空间查询中的空间关系计算转换为字段查询，从而降低了复杂性。
of the spatial database index, lessening the computational load of queries, and enhancing retrieval efficiency. 空间数据库索引的优化，减少查询的计算负载，并提升检索效率。
4.1.3. Comparison of database capacity consumption 4.1.3. 数据库容量消耗对比
The database capacity sizes of Oracle Spatial and Oracle GGRN corresponding to Experimental Data 1, Experimental Data 2, and Experimental Data 3 are shown in Fig. 6. The database capacity of Oracle GGRN is smaller than that of Oracle Spatial. Table 11 shows that, compared with Oracle Spatial, Oracle GGRN saves 5.56 %, 68.00 %, and 66.32 % in database capacity consumption for experimental datasets 1, 2 , and 3 , respectively, resulting in average savings of 46.63%46.63 \%. This indicates that in the Oracle database, the UMMG not only improves the efficiency of ULI retrieval but also reduces index complexity, thereby reducing the consumption of ULI in computer storage space. Oracle Spatial 和 Oracle GGRN 对应于实验数据 1、实验数据 2 和实验数据 3 的数据库容量大小如图 6 所示。Oracle GGRN 的数据库容量小于 Oracle Spatial。表 11 显示，与 Oracle Spatial 相比，Oracle GGRN 在实验数据集 1、2 和 3 中分别节省了 5.56%、68.00%和 66.32%的数据库容量消耗，平均节省量为 46.63%46.63 \% 。这表明在 Oracle 数据库中，UMMG 不仅提高了 ULI 检索效率，还降低了索引复杂度，从而减少了 ULI 在计算机存储空间中的占用。
PostgreSQL is an object-oriented relational database management system developed based on POSTGRES 4.2 from the Department of Computer Science at the University of California. It supports triggers, views, complex queries, and multiversion concurrency control (Viloria PostgreSQL 是一个基于加州大学计算机科学系开发的 POSTGRES 4.2 版本的对象导向关系型数据库管理系统。它支持触发器、视图、复杂查询以及多版本并发控制（MVCC）。
Fig. 5. Average retrieval times for Oracle Spatial and Oracle GGRN in experimental data 3. 图 5. 实验数据 3 中 Oracle Spatial 和 Oracle GGRN 的平均检索时间。
Experimental data Experimental data 1 Experimental data 2 Experimental data 3 Average improvement
C_(d) 5.56% 68.00% 66.32% 46.63%| Experimental data | Experimental data 1 | Experimental data 2 | Experimental data 3 | Average improvement |
| :--- | :--- | :--- | :--- | :--- |
| $C_{d}$ | $5.56 \%$ | $68.00 \%$ | $66.32 \%$ | $46.63 \%$ |
et al., 2019). PostGIS is a spatial extension of PostgreSQL that provides spatial information services, such as spatial objects, spatial indexes, spatial operators, and spatial operation functions (Meyer and Brunn, 2019). This study used PostgreSQL’s data batch fast import instruction “copy_from” to implement experimental data entry. The entry times of the experimental data are listed in Table 12. 等，2019）。PostGIS 是 PostgreSQL 的空间扩展，提供空间信息服务，包括空间对象、空间索引、空间运算符和空间操作函数（Meyer 和 Brunn，2019）。本研究使用 PostgreSQL 的数据批量快速导入指令“copy_from”实现实验数据录入。实验数据的录入时间如表 12 所示。
4.2.1. Index establishment time 4.2.1. 索引建立时间
In the PostgreSQL database, PostgreSQL + PostGIS uses a Generalized Search Tree (GIST) index (Gerdjikov et al., 2013; Binder et al., 2009). The GIST index defines a rule to distribute any type of data across 在 PostgreSQL 数据库中，PostgreSQL + PostGIS 使用通用搜索树 (GIST) 索引（Gerdjikov 等，2013；Binder 等，2009）。GIST 索引定义了一条规则，用于将任何类型的数据分布到
Table 12 表 12
Entry times for experiment data. 实验数据的录入时间。
Experimental data 实验数据
Experimental data 实验数据
Experimental data 实验数据
Experimental data 实验数据
1
2
3
Entry time (s) 入场时间（秒）
5.77
31.32
64.51
Experimental data Experimental data Experimental data Experimental data
1 2 3
Entry time (s) 5.77 31.32 64.51| Experimental data | Experimental data | Experimental data | Experimental data |
| :--- | :--- | :--- | :--- |
| | 1 | 2 | 3 |
| Entry time (s) | 5.77 | 31.32 | 64.51 |
a balanced tree and defines a method to use this representation for operator access. The index establishment times for experimental datasets 1, 2, and 3 using PostgreSQL + PostGIS and PostgreSQL GGRN are listed in Table 13. The index establishment times for PostgreSQL + PostGIS and PostgreSQL GGRN increased with the spatial data volume. Using the same experimental data, the index establishment time of Oracle GGRN was approximately one-third of that of Oracle Spatial. Oracle GGRN significantly reduces the time cost of establishing a 一个平衡树，并定义了一种使用此表示方法进行操作符访问的方法。使用 PostgreSQL + PostGIS 和 PostgreSQL GGRN 对实验数据集 1、2 和 3 进行索引建立的时间如表 13 所示。PostgreSQL + PostGIS 和 PostgreSQL GGRN 的索引建立时间随空间数据量增加而增加。使用相同的实验数据，Oracle GGRN 的索引建立时间约为 Oracle Spatial 的三分之一。Oracle GGRN 显著降低了建立索引的时间成本。
Table 13 表 13
Index establishment times of PostgreSQL + PostGIS and PostgreSQL GGRN. PostgreSQL + PostGIS 和 PostgreSQL GGRN 的索引建立时间。
Experimental data 实验数据
Experimental data 1 实验数据 1
Experimental data 2 实验数据 2
Experimental data 3 实验数据 3
Index establishment time of PostgreSQL + PostGIS (s) PostgreSQL + PostGIS 的索引建立时间（秒）
28.86
168.06
317.07
Index establishment time of PostgreSQL GGRN (s) PostgreSQL GGRN 索引建立时间（秒）
8.61
56.54
112.38
Experimental data Experimental data 1 Experimental data 2 Experimental data 3
Index establishment time of PostgreSQL + PostGIS (s) 28.86 168.06 317.07
Index establishment time of PostgreSQL GGRN (s) 8.61 56.54 112.38| Experimental data | Experimental data 1 | Experimental data 2 | Experimental data 3 |
| :--- | :--- | :--- | :--- |
| Index establishment time of PostgreSQL + PostGIS (s) | 28.86 | 168.06 | 317.07 |
| Index establishment time of PostgreSQL GGRN (s) | 8.61 | 56.54 | 112.38 |
Table 14 表 14
Retrieval times for PostgreSQL + PostGIS and PostgreSQL GGRN in experimental data 1. PostgreSQL + PostGIS 和 PostgreSQL GGRN 在实验数据 1 中的检索时间
ID
Retrieval time for PostgreSQL + PostGIS (ms) PostgreSQL + PostGIS 的检索时间（毫秒）
Retrieval time for PostgreSQL GGRN (ms) PostgreSQL GGRN 的检索时间（毫秒）
PostgreSQL + PostGIS and PostgreSQL GGRN randomly selected ten SPRNs from experiment data 1,2 , and 3 for spatial retrieval experiments. The retrieval time was the average of three queries under the same conditions. The PostgreSQL + PostGIS and PostgreSQL GGRN retrieval times for experimental data 1 are listed in Table 14, and the average retrieval times for the 10 SPRNs are shown in Fig. 7. PostgreSQL + PostGIS 和 PostgreSQL GGRN 从实验数据 1、2 和 3 中随机选取了 10 个 SPRN 进行空间检索实验。检索时间为在相同条件下三次查询的平均值。PostgreSQL + PostGIS 和 PostgreSQL GGRN 在实验数据 1 中的检索时间如表 14 所示，10 个 SPRNs 的平均检索时间如图 7 所示。
The PostgreSQL + PostGIS and PostgreSQL GGRN retrieval times for experimental data 2 are listed in Table 15, and the average retrieval times for the ten SPRNs are shown in Fig. 8. PostgreSQL + PostGIS 和 PostgreSQL GGRN 对于实验数据 2 的检索时间如表 15 所示，而 10 个 SPRN 的平均检索时间如图 8 所示。
The PostgreSQL + PostGIS and PostgreSQL GGRN retrieval times for experimental data 3 are listed in Table 16, and the average retrieval times for the ten SPRNs are shown in Fig. 9. PostgreSQL + PostGIS 和 PostgreSQL GGRN 对于实验数据 3 的检索时间如表 16 所示，而十个 SPRN 的平均检索时间如图 9 所示。
From Table 17, it is evident that, compared with PostgreSQL + PostGIS, PostgreSQL GGRN improves retrieval efficiency by 7.03%7.03 \%, 5.63%5.63 \%, and 3.21%3.21 \% for experimental data 1, experimental data 2, and experimental data 3, respectively, resulting in an average improvement of 5.29%5.29 \%. PostgreSQL GGRN demonstrated a notable improvement in the retrieval of different spatial data volumes compared with PostgreSQL + PostGIS. The GIST index used by PostgreSQL + PostGIS is effective for spatial indexing, highlighting the feasibility of PostgreSQL GGRN in this area. 从表 17 可以看出，与 PostgreSQL + PostGIS 相比，PostgreSQL GGRN 在实验数据 1、实验数据 2 和实验数据 3 中分别提高了 7.03%7.03 \% 、 5.63%5.63 \% 和 3.21%3.21 \% 的检索效率，平均提升了 5.29%5.29 \% 。PostgreSQL GGRN 在处理不同空间数据量时的检索性能显著优于 PostgreSQL + PostGIS。PostgreSQL + PostGIS 所使用的 GIST 索引在空间索引方面表现有效，这进一步证明了 PostgreSQL GGRN 在该领域的可行性。
4.2.3. Comparison of database capacity consumption 4.2.3. 数据库容量消耗对比
The database capacity sizes of PostgreSQL + PostGIS and PostgreSQL GGRN corresponding to experimental data 1 , experimental data 2 , and experimental data 3 are presented in Fig. 10. The database capacity of PostgreSQL GGRN is smaller than that of PostgreSQL + PostGIS. Table 18 shows that compared with PostgreSQL + PostGIS, PostgreSQL GGRN achieved savings of 61.26%,61.15%61.26 \%, 61.15 \%, and 61.53%61.53 \% in database capacity consumption for experimental datasets 1,2 , and 3 , respectively, resulting in average savings of 61.31 %. This indicates that in the PostgreSQL database, the creation of the GIST index requires more time and space, and the UMMG improves the efficiency of ULI retrieval to a certain extent while significantly reducing the consumption of ULI in computer storage space. PostgreSQL + PostGIS 和 PostgreSQL GGRN 对应于实验数据 1、实验数据 2 和实验数据 3 的数据库容量大小如图 10 所示。PostgreSQL GGRN 的数据库容量小于 PostgreSQL + PostGIS。表 18 显示，与 PostgreSQL + PostGIS 相比，PostgreSQL GGRN 在实验数据集 1、2 和 3 中分别节省了 61.26%,61.15%61.26 \%, 61.15 \% 和 61.53%61.53 \% 的数据库容量消耗，平均节省了 61.31%。这表明在 PostgreSQL 数据库中，创建 GIST 索引需要更多时间和空间，而 UMMG 在一定程度上提高了 ULI 检索效率，同时显著减少了 ULI 在计算机存储空间中的消耗。
4.3. Analysis of comprehensive performance 4.3. 综合性能分析
As shown in Table 19, the overall performance of Oracle GGRN was P_(c)=43.00%P_{c}=43.00 \%, indicating that Oracle GGRN outperformed Oracle Spatial in terms of time and space consumption. The comprehensive performance of PostgreSQL GGRN was P_(c)=33.30%P_{c}=33.30 \%, indicating that PostgreSQL GGRN outperformed PostgreSQL + PostGIS in terms of time and space consumption. The above experiment demonstrated the feasibility of the UMMG, which performed well in terms of both retrieval time and storage space consumption. It can be observed that the UMMG 如表 19 所示，Oracle GGRN 的整体性能为 P_(c)=43.00%P_{c}=43.00 \% ，表明 Oracle GGRN 在时间和空间消耗方面优于 Oracle Spatial。PostgreSQL GGRN 的综合性能为 P_(c)=33.30%P_{c}=33.30 \% ，表明 PostgreSQL GGRN 在时间和空间消耗方面优于 PostgreSQL + PostGIS。上述实验证明了 UMMG 的可行性，其在检索时间和存储空间消耗方面均表现良好。可以观察到，UMMG
Table 15 表 15
Retrieval times for PostgreSQL + PostGIS and PostgreSQL GGRN in experimental data 2. PostgreSQL + PostGIS 和 PostgreSQL GGRN 在实验数据 2 中的检索时间。
ID
Retrieval time for PostgreSQL + PostGIS (ms) PostgreSQL + PostGIS 的检索时间（毫秒）
Retrieval time for PostgreSQL GGRN (ms) PostgreSQL GGRN 的检索时间（毫秒）
Fig. 7. Average retrieval times for PostgreSQL + PostGIS and PostgreSQL GGRN in experimental data 1. 图 7. 实验数据 1 中 PostgreSQL + PostGIS 与 PostgreSQL GGRN 的平均检索时间。
Fig. 8. Average retrieval times for PostgreSQL + PostGIS and PostgreSQL GGRN in experimental data 2. 图 8. 实验数据 2 中 PostgreSQL + PostGIS 与 PostgreSQL GGRN 的平均检索时间。
Table 16 表 16
Retrieval times for PostgreSQL + PostGIS and PostgreSQL GGRN in experimental data 3. PostgreSQL + PostGIS 和 PostgreSQL GGRN 在实验数据 3 中的检索时间。
ID
Retrieval time for PostgreSQL + PostGIS (ms) PostgreSQL + PostGIS 的检索时间（毫秒）
Retrieval time for PostgreSQL GGRN (ms) PostgreSQL GGRN 的检索时间（毫秒）
effectively addresses the challenge of precise location cognition between humans and machines while also reducing the complexity of spatial database indexing. 有效解决了人类与机器之间精准位置认知挑战，同时简化了空间数据库索引的复杂性。
5. Conclusion 5. 结论
This study defines the GGRN and its corresponding code, introduces the GGRN logical structure and spatial hierarchy, and proposes GGRN code generation methods. Based on this, a method for organizing the ULI based on the GGRN was constructed. GGRN provides data-indexing support for ULI. ULI within the same geospatial grid corresponds to a unique GGRN that achieves query statistics and real-time sharing of the ULI. Moreover, GGRN binary encoding can provide more efficient services because of its fast retrieval. 本研究定义了 GGRN 及其对应的编码，介绍了 GGRN 的逻辑结构和空间层次，并提出了 GGRN 编码生成方法。在此基础上，构建了基于 GGRN 的 ULI 组织方法。GGRN 为 ULI 提供了数据索引支持。同一地理空间网格内的 ULI 对应唯一的 GGRN，从而实现 ULI 的查询统计与实时共享。此外，GGRN 的二进制编码可通过快速检索提供更高效的服务。
This study used UDAC as an example to conduct an experimental analysis of the efficiency of organizing, managing, and retrieving ULI based on the GGRN, verifying the feasibility and correctness of the proposed GGRN expression and ULI organization. As a carrier of the ULI grid representation, USG replaces the spatial relation calculation operation with the GGRN query method, reducing the complexity of spatial database indexing and effectively solving the problem of precise location cognition between humans and machines. Future work will investigate methods to further optimize the performance and scalability of the GGRN system, especially when handling large datasets and real-time applications. 本研究以 UDAC 为例，基于 GGRN 对 ULI 的组织、管理和检索效率进行了实验分析，验证了所提出的 GGRN 表达方式及 ULI 组织方案的可行性和正确性。作为 ULI 网格表示的载体，USG 用 GGRN 查询方法替代了空间关系计算操作，简化了空间数据库索引的复杂性，有效解决了人类与机器之间精准定位认知的问题。未来研究将探索进一步优化 GGRN 系统性能和可扩展性的方法，尤其是在处理大规模数据集和实时应用场景时。
Fig. 9. Average retrieval times for PostgreSQL + PostGIS and PostgreSQL GGRN in experimental data 3. 图 9. 实验数据 3 中 PostgreSQL + PostGIS 与 PostgreSQL GGRN 的平均检索时间。
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. 作者声明，他们没有已知的任何可能影响本论文中所报告工作结果的财务利益冲突或个人关系。
Acknowledgements 致谢
This research was funded by the National Key Research and Development Program of China, grant number 2018YFB0505300, the National Natural Science Foundation of China, grant number 62332014, the talent startup fund of Fuzhou University, grant number 511182, the National Natural Science Foundation of China, grant number 62371135, and the Natural Science Foundation of Fujian Province, grant number 2023J01431. 本研究得到国家重点研发计划（项目编号：2018YFB0505300）、国家自然科学基金（项目编号：62332014）、福州大学人才启动基金（项目编号：511182）中国国家自然科学基金（项目编号：62371135），以及福建省自然科学基金（项目编号：2023J01431）。
Data availability 数据可用性
The data that has been used is confidential. 所使用的数据属于机密信息。
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Abbreviations: ARN, Area Region Name; DGGS, Discrete Global Grid System; DNS, Domain Name System; GGC, Geospatial Grid Code; GGRN, Geospatial Grid Region Name; PRN, Personal Region Name; RRN, Root Region Name; ORN, Organization Region Name; ULI, Ubiquitous Location Information; UDAC, Universal Delivery Address Coding. 缩写：ARN，区域名称；DGGS，离散全球网格系统；DNS，域名系统；GGC，地理空间网格代码；GGRN，地理空间网格区域名称；PRN，个人区域名称；RRN，根区域名称；ORN，组织区域名称；ULI，无处不在的位置信息；UDAC，通用交付地址编码。
