Conventional network analysis functions and related algorithms in GIS

Conventional network analysis functions and related algorithms in GIS

Source: http://www.legalsoft.com.cn
Author: Zeng wenxu shiwen

Abstract network is a unique data entity in GIS. network analysis is an important aspect of spatial analysis. the General GIS platform software provides the following network analysis functions: Path Analysis, resource allocation, connectivity analysis, stream analysis, and site selection. Many of these functions can be implemented using algorithms in graph theory. an important algorithm for implementing these functions is briefly introduced.

Key words network, network analysis, geographic information system (GIS), graph theory.

0 Introduction
　　
Network analysis is an important aspect of spatial analysis. It is based on the network topology relationship (the connection and connection between linear entities and nodes, and between nodes ), by examining the space and attribute data of network elements, the network performance features are analyzed and calculated in many aspects.

Compared with other GIS analysis functions, network analysis has been rarely studied. However, in recent years, due to the widespread use of GIS management
Mesh facilities (such as various underground pipelines, transportation lines, and communication lines in the city) increase the demand for network analysis functions rapidly, GIS platform software has released its own network analysis subsystem [1] ①.
Compared with the increasing research on network analysis in the world, several influential GIS systems in China have begun to provide more or less network analysis functions. It should be noted that the domestic applications and needs are also quite extensive and
This will certainly play a huge role in promoting the research of network analysis.

1. Network Data Model-Several Basic Concepts
　　
A network is a system composed of multiple linear entities. Resources are transmitted by the network, and the links between entities are also transmitted by the network.
. The network data model is an abstract representation of Network Systems in the real world (such as traffic network, communication network, tap water pipe network, and Gas Pipe Network. the most basic element of the network is the above linear entities and the entities
The connection point. The former is often called a network cable or link, and the latter is generally called a node ).

A network cable forms the skeleton of the network. It is a channel for resource transmission or communication. It can represent highways, railways, routes, water pipes, gas pipes, and rivers. A node is the endpoint of the network cable and the convergence point of the network cable, it can represent intersections, transfer stations, and river points.

In addition to the above basic network elements, the Network may also have a number of ancillary elements, such as the site (STOP) used in Path Analysis to indicate the locations through which resources can be loaded and unloaded ); in resource allocation, it is used to represent the center (cen_ter) of the resource divergence location or the resource aggregation location, and barrier blocks the resource transmission or communication.

　
For network analysis, the network cable or node, as the basic element of the network, has some special attribute data besides its common attributes. for example, to implement path analysis and resource allocation, network cable data should be packaged
It includes both positive and negative obstacles (such as flow time and consumption) and resource demand (such as number of students, water flow, and customer volume), and node data should also include resource demand. especially in some GIS
In the Platform (such as ARC/INFO, MAPGIS), the node can also have corner data, which can simulate the turning characteristics of resource flow in more detail. specifically, each node can have
A forward table (turntable), each of which indicates the obstacle strength of resources from a certain network line to another network line.

Due to different versatility and network
Different geographic information systems have different network models. The differences are mainly reflected in the classification and setting of network affiliated elements. for affiliated network elements, data packets associated with the center
Including the resource capacity and obstacles of the center (the maximum cumulative obstacles that can be overcome by resource outflow or flow to the center). Some GIS systems also allow some delays to the center, to indicate that this center is relative to other centers
Priority of resource allocation. Generally, site-related data is transferred (that is, the amount of resource loading and unloading), which hinders the strength of the Data. barriers generally do not require any relevant data.

2. Conventional Network Analysis

2.1 Path Analysis

Path analysis is the most basic function in GIS. Its core is to solve the optimal path and shortest path. From the perspective of the network model, the optimal path Solution
It is to find a path between the two nodes in the specified network with the least barrier strength. the Optimal Path is generated based on the network cable and the corner of the node (if the node in the model has corner data. for example, if you want to find the fastest
Path, the obstacle strength should be set to the time spent by turning through the network cable or at the node; if you want to find the path with the minimum cost, the obstacle strength should be the cost. when the network cable is in the forward and backward directions
The optimal path is the shortest path when the length of the network cable and no corner data at the node or the corner data is 0. in some cases, the user may require the system to find the optimal path between all node pairs at a time, or
Understand the Optimal Path of the second, third, and K between the two nodes.

Another path analysis function is the solution to the best travel solution. The solution to the best travel solution of the network cable is to give a network cable
The set and a node are used to find the optimal path, so that the specified node can go through each network cable at least once and return to the Start Node. the best travel solution for a node is to specify a starting node, a ending node, and
Work on the intermediate node to find the optimal path, so that all the intermediate nodes can be traversed from the starting point to reach the end point.

2.2 Resource Allocation

Resource allocation is in the Network
Find the nearest network cable and node (here the distance is determined by the size of the obstacle strength) Center (resource divergence or collection location ). for example, resource allocation can help students in every street in the city determine the nearest course.
School, provide its water supply area for the reservoir, and so on. resource allocation is to simulate how resources are distributed in the center (school, fire station, reservoir, etc.) and the Network cables (streets, waterways, etc.), nodes (intersections, bus transfer stations, etc.) around it)
Between. network cables and nodes are allocated to the center based on the center capacity and network cable and node requirements. The distribution is performed along the optimal path. when a network element is assigned to a center, the resources of the center are based on
The demand for network elements is reduced. When the resources in the center are exhausted, the allocation is stopped. You can control the allocation scope by assigning obstacles to the center.

2.3 connectivity analysis

People often need to know all the nodes or network cables that can be reached from a certain node or network cable. this type of problem is called the Connected Component solution. another connectivity analysis problem is the solution of the least-cost connectivity solution, that is, to connect all nodes with each other at the minimum cost.

2.4 Stream Analysis

　
A stream is to transport resources from one location to another. the problem of stream analysis is mainly to design a transportation solution according to a certain optimization standard (minimum time, minimum cost, minimum distance or maximum shipping volume.
To implement stream analysis, we need to expand the network model according to different optimization standards. The center should be divided into the receiving center and the delivery center, representing the starting point and target point of resource delivery respectively. the capacity of the shipping center represents
Amount of resources to be shipped. The capacity of the shipping center represents the amount of resources it needs. the data related to the network cable also needs to be expanded. If the optimal standard is that the maximum traffic is sent, the transmission capability of the network cable should be set; if the goal is to make the most cost
Low, you need to set the transmission cost for the network cable (the cost required to transport a unit of resources online on the network ).

Site selection 2.5

The site selection function involves
Select the location of service facilities in a specific area, such as the suburban store area, fire station, factory, airport, and warehouse. [2]. in network analysis, the site selection problem is generally limited to that the facility must be located in a certain
The node is located on a certain online network, or is limited to a number of candidate locations. there are many kinds of site selection problems and various implementation methods and techniques. Different GIS systems have their own characteristics in this respect. this causes many
The main reason for this is the explanation of "optimal location" (that is, the criteria used to measure the advantages and disadvantages of a location), and whether a facility or multiple facilities are to be located.

3. Network Analysis Algorithms
　　
From the mathematical point of view, we can look at the graph in GIS, so we can use the research results of graph theory to solve this problem.
Many problems in network analysis. the term "network" in graph theory refers to a weighted directed graph. However, the networks involved in GIS have the following special characteristics compared with the graphs or networks discussed in mathematics. (1) network cable and Node
Is meaningful. (2) except that the network cable can have a weight value, the node can also have a weight value, and the weight value may be multiple, for example, the network cable can have forward and reverse obstacles to strength, demand, capacity, and consumption.
And so on. (3) The node may have corner data. (4) networks in GIS are not always directed graphs. for water systems, gas pipeline systems, and other networks, the flow of contents in the network is fixed, and
The flow direction is also an important basis for relevant analysis, so they should be investigated as Directed Graphs. However, networks like the urban road network should be considered as undirected graphs, and several one-way streets should be considered, can be blocked by the network cable strength
To define the direction.
Despite the above differences, many algorithms in graph theory can still be used for network analysis. Of course, some algorithms must be modified or expanded based on the actual situation.

　
The optimal path problem is the most thoroughly studied in graph theory. There are dozens of solutions [3]. The Dijkstra algorithm is widely used in GIS systems. Its basic idea is to find the starting point from near to far.
The Dijkstra algorithm also plays an important role in solving the resource allocation scheme, because the search process is being distributed from the central node to the target node.
The method is consistent. for solving the optimal distance between two nodes, the Floyd algorithm or dantzig algorithm is often used. They all start to iterate repeatedly from the graph's Adjacent matrix, and finally get the distance matrix. Double Scan
The algorithm (double_sweep algorithm) can be used to obtain the k Shortest Path Between a node and other nodes.

In graph theory, the solution to the optimal travel network cable solution is called the China mail route problem. It is a problem related to both the Euler's graph and the optimal path, you can use the "parity graph job method" to obtain the optimal closed path.

　
The node traveling question is similar to the famous Salesman Problem in graph theory (TSP, that is, finding the optimal closed path after each node). The TSP algorithm can be used by the Best Traveler at the node after proper modification.
Solution. TSP is an NP-complete problem [4]. Generally, the approximate optimal solution can only be found using the approximate solution. better approximate solutions include greedy-based closest point Link Method and optimal insertion method, and heuristic search
The Branch and limit methods of the cable strategy, such as the edge exchange adjustment method based on the local search policy, can often get quite satisfactory results.

The connectivity analysis problem corresponds to the graph generation tree solution. the connected component usually uses depth-first traversal or breadth-first traversal to form the depth or breadth-first spanning tree. the minimum cost connection solution is to solve the optimal Spanning Tree of the graph. The prim algorithm or Kruskal algorithm is generally used.

　
In graph theory, the network used for stream analysis is called a capacity network with receiving and receiving points. The research on this network forms the network stream theory, which is one of the hot topics in graph theory. when the optimal transport scheme is the largest transport volume,
It can be solved using the maximum flow algorithm proposed by Ford and Fulkerson (according to [5]). It is based on the maximum flow least cut theorem, by searching for the incrementing path, using the method of gradually increasing the stream Value
Find the largest stream. Ford and Fulkerson, promote the above algorithms, and obtain the minimum cost flow algorithm, which can be used in the design of transmission solutions under other optimization standards.

　
The solution and complexity vary greatly depending on the specific requirements of site selection. if the facility is confined to the node, and the site selection criterion is the least distance from the farthest node (to ensure timely response, the fire station
It may be based on the Standard Site Selection), you only need to find the distance between any node pairs and establish a distance matrix. The positioning point is the node corresponding to the minimum value of each element in each line of this matrix. other problems regarding the positioning of a single facility
However, it may be more complex than the above example, but it can always be solved. In contrast, it is much more difficult to select several facility locations at the same time, and almost always relies on Integer Programming to solve the problem [3].

4 Conclusion
　　
Although a large number of algorithms obtained in graph theory research can provide powerful theoretical support for network analysis, as described above
There is a certain gap in the mathematical model, which sometimes has a great impact on network analysis. in addition, most of the problems discussed above are the optimization of combinations. In actual network engineering applications, there are other problems involving a large amount of computing.
Such as System Stability Analysis and running status analysis. Therefore, when applying Graph Theory Algorithms to meet the needs of network analysis, we should also consider looking for more extensive mathematical models and mathematical methods.
For example, we can combine Graph Theory with System Theory to regard a network as a system and use network elements as system units, use a terminal diagram and a group of first-order differential equations or a group of algebraic Simultaneous Equations containing terminal variables to express the network
Networking and solving related problems [6]. it is worth noting that the rapid development of electric network theory leads to the emergence of a series of analysis methods. How to apply it to GIS network analysis is also a very meaningful research course.
Question.

References
1 ESRI. network analysis guide. Redlands, CA: Environmental Systems Research Institute, 1995-12 ~ 22
2 ESRI. location_allocation in ArcInfo. Redlands, CA: Environmental Systems Research Institute, 1995-2 ~ 10
3 minieka E; Li jiaxiao, Zhao Guanqi. Network and graph optimization algorithms. Beijing: China Railway Publishing House, 1984-36 ~ 73,277 ~ 302
4
Hopcroft j e, Ullman j d. Introduction to automatic theory, ages,
And computation. Reading, Mass: addison_wesley Publishing Co, 1979.
332 ~ 336
5 Dynasty: Swiss. graph theory. Beijing: Beijing Institute of Industry Press, 1986-297 ~ 308

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