【第九章知识点总结1】9.1 Motivation and use cases 9.2 Conceptual model

9.1 Motivation and use cases（动机与应用场景）

一、核心动机

1. 传统技术局限性 ：
   • OGIS 简单要素类型仅支持几何对象（点、线、面等），缺乏图数据类型和最短路径等网络分析算子；
   • 传统 SQL 仅支持选择、投影、连接、统计等基础操作，缺少传递闭包功能，无法满足网络分析需求（SQL3 新增递归与传递闭包特性弥补该缺陷）。
2. 现实需求驱动：导航是人类核心活动（从历史贸易路线、军事路线到现代消费平台），空间网络分析需解决传统技术无法支撑的复杂空间关联问题。

二、典型应用场景

1. 导航与路径规划（Routes） ：
   • 计算起点到终点的最短路径；
   • 规划覆盖多个目的地的最短路线；
   • 按驾驶距离查找最近的目的地（如医院）；
   • 包裹配送路线优化。
2. 资源分配（Allocation） ：
   • 将客户分配给最近的服务中心；
   • 绘制每个服务中心的服务范围。
3. 选址分析（Site Selection） ：
   • 为新服务中心选择最优位置（基于客户分布和数量需求）。
4. 基于位置的服务（LBS） ：
   • 定位服务（地理编码：地名 / 地址→经纬度；反向地理编码：经纬度→地名）；
   • 周边查询（如 1 英里内的所有银行、最近的诊所 / 餐厅 / 出租车）；
   • 细分场景：休闲娱乐型（签到、大富翁游戏）、生活服务型（周边服务搜索、旅游结合、票务）、社交型（地点交友、地理社区）、商业型（团购、优惠推送、店内模式）。
5. 特定网络查询示例 ：
   • 铁路网络：查询黄西（YW）路线的站点数量、从伯克利市中心（2 号站点）可达的所有站点、连接伯克利市中心与戴利城（5 号站点）的路线编号、蓝西（BW）路线的终点站；
   • 河流网络：查询密西西比河的所有直接 / 间接支流名称、科罗拉多河的直接支流、北普拉特河发生泄漏时可能受影响的河流。
6. 行业落地场景：空间网络广泛应用于交通、能源、水利、通信、农业、金融、商业设施、应急服务、医疗健康、信息技术等现代社会关键领域。

9.2 Conceptual model（概念模型）

一、模型核心定义

概念模型是空间网络的抽象表达框架，包含信息模型和数学模型两大核心维度，用于明确空间网络的核心实体、关系及数学逻辑。

二、两大核心组成

1. 信息模型（Entity Relationship Diagrams，实体关系图） ：
   • 核心实体：道路（含街道、大道）、道路交叉口、道路路段、转弯、兴趣点、地址、观察者等；
   • 关联属性：坐标系统、路线、转向信息、街道地名录、行驶时间、参考段序列、符号 / 数值标识等；
   • 核心逻辑：通过实体间的关联关系（如道路与交叉口的连接、路段与转向的关联）描述空间网络的结构。
2. 数学模型（Graphs，图模型） ：
   • 定义：图 \(G=(V, E)\)，其中 V 为有限顶点集，E 为边集，用于表示顶点间的二元关系；
   • 实例应用：河流网络中，顶点表示河流，边表示 "一条河流汇入另一条河流" 的关系；道路网络中可通过顶点和边描述路段、交叉口的连接关系。

三、图模型的优缺点

1. 优势 ：
   • 具备完善的数学推理基础；
   • 拥有丰富的计算算法和数据结构支持。
2. 不足 ：
   • 仅能建模单一二元关系；
   • 难以表达多维度关系（如道路网络中的 "连接" 与 "转向" 同时存在的场景）；
   • 同一空间网络可能对应多种图模型设计（需根据需求选择）。

四、道路网络的图模型设计方案（针对 "转向" 建模优化）

1. 方案 1：顶点 = 道路交叉口，边 (A,B)= 连接相邻交叉口 A、B 的道路路段；
2. 方案 2：顶点 = 有向道路路段，边 (A,B)= 从路段 A 到路段 B 的转向；
3. 方案 3：顶点 = 道路，边 (A,B)= 道路 A 与道路 B 的相交关系；
4. 补充方案：使用超边（超图）或在图顶点中嵌入转向信息，解决传统图模型难以表达转向关系的问题。

9.1 Motivation and use cases

I. Core Motivation

1. Limitations of Traditional Technologies :
   • OGIS Simple Feature Types only support geometric objects (points, line strings, polygons, etc.) but lack graph data types and network analysis operators such as shortest path.
   • Traditional SQL only supports basic operations like select, project, join, and statistics, and lacks transitive closure functionality, which cannot meet the needs of network analysis (SQL3 adds recursion and transitive closure features to make up for this defect).
2. Driven by Practical Needs: Navigation is a core human activity (from historical trade routes and military routes to modern consumer platforms). Spatial network analysis needs to solve complex spatial correlation problems that cannot be supported by traditional technologies.

II. Typical Application Scenarios

1. Navigation and Route Planning (Routes) :
   • Calculate the shortest path from the starting point to the destination.
   • Plan the shortest route covering multiple destinations.
   • Find the nearest destination (e.g., hospital) by driving distance.
   • Optimization of package delivery routes.
2. Resource Allocation (Allocation) :
   • Assign customers to the nearest service centers.
   • Map the service area of each service center.
3. Site Selection Analysis (Site Selection) :
   • Select the optimal locations for new service centers (based on customer distribution and quantity requirements).
4. Location-Based Services (LBS) :
   • Positioning services (geocoding: place name/address → latitude and longitude; reverse geocoding: latitude and longitude → place name).
   • Surrounding queries (e.g., all banks within 1 mile, the nearest clinic/restaurant/taxi).
   • Sub-scenarios: Leisure and entertainment (check-in, Monopoly-style games), lifestyle services (surrounding service search, combination with travel, ticketing), social (location-based dating, geographic communities), commercial (group buying, discount push, in-store mode).
5. Specific Network Query Examples :
   • Railway Network: Query the number of stops on the Yellow West (YW) route, all stops accessible from Downtown Berkeley (Stop 2), the route numbers connecting Downtown Berkeley and Daly City (Stop 5), and the terminal stop of the Blue West (BW) route.
   • River Network: List the names of all direct and indirect tributaries of the Mississippi River, the direct tributaries of the Colorado River, and the rivers that might be affected if there is a spill in the North Platte River.
6. Industry Application Scenarios: Spatial networks are widely used in key areas of modern society such as transportation, energy, water conservancy, communications, agriculture, finance, commercial facilities, emergency services, healthcare, and information technology.

9.2 Conceptual model

I. Core Definition of the Model

The conceptual model is an abstract expression framework for spatial networks, including two core dimensions: information model and mathematical model, which are used to clarify the core entities, relationships, and mathematical logic of spatial networks.

II. Two Core Components

1. Information Model (Entity Relationship Diagrams) :
   • Core Entities: Roads (including streets, avenues), road intersections, road segments, turns, points of interest, addresses, observers, etc.
   • Associated Attributes: Coordinate system, routes, turn information, street gazetteers, travel time, reference segment sequences, symbolic/numeric identifiers, etc.
   • Core Logic: Describe the structure of spatial networks through the association relationships between entities (e.g., the connection between roads and intersections, the association between road segments and turns).
2. Mathematical Model (Graphs) :
   • Definition: A graph \(G=(V, E)\), where V is a finite set of vertices and E is a set of edges used to represent binary relationships between vertices.
   • Practical Application: In a river network, vertices represent rivers, and edges represent the relationship of "one river flowing into another river"; in a road network, vertices and edges can be used to describe the connection relationships between road segments and intersections.

III. Advantages and Disadvantages of Graph Models

1. Advantages :
   • Equipped with a sound mathematical reasoning foundation.
   • Supported by a rich set of computational algorithms and data structures.
2. Disadvantages :
   • Can only model a single binary relationship.
   • Difficult to express multi-dimensional relationships (e.g., scenarios where "connection" and "turn" coexist in a road network).
   • Multiple graph model designs may correspond to the same spatial network (selection needs to be based on requirements).

IV. Graph Model Design Schemes for Road Networks (Optimized for Turn Modeling)

1. Scheme 1: Vertices = road intersections; Edge (A, B) = road segment connecting adjacent intersections A and B.
2. Scheme 2: Vertices = (directed) road segments; Edge (A, B) = turn from road segment A to road segment B.
3. Scheme 3: Vertices = roads; Edge (A, B) = road A intersects with road B.
4. Supplementary Scheme: Use hyper-edges (and hyper-graphs) or embed turn information in graph vertices to solve the problem that traditional graph models are difficult to express turn relationships.