A method for generating and quantitatively evaluating planar graph networks of varying complexity.

Abstract

This invention discloses a method for generating and quantitatively evaluating planar graph networks of varying complexities. The generation method includes the following steps: S1: Determine the boundary of the simulation area based on the traffic scenario and target requirements, and generate a point set within the simulation area; S2: Generate a planar graph network of maximum complexity on the point set using the Delaunay triangulation algorithm. The planar graph network of maximum complexity includes edges and all points in the point set, with edges obtained by connecting the points in the point set; S3: Process the planar graph network of maximum complexity based on the edge data to generate planar graph networks of different complexities. This invention can quickly create a high-complexity network containing the maximum number of edges while ensuring its planarity; it allows users to dynamically reduce the complexity of the network as needed, generating a series of networks with different complexities, thereby providing a more diverse simulation environment and enabling flexible simulation of complex dynamic changes in traffic flow.

Description

Technical Field

[0001] This invention relates to the field of intelligent transportation technology, and in particular to a method for generating and quantitatively evaluating planar graph networks of varying complexity. Background Technology

[0002] With the acceleration of global urbanization and the widespread use of motor vehicles, many cities are facing the challenge of traffic congestion. This congestion not only prolongs travel time but also increases fuel consumption and pollution emissions, while also negatively impacting the quality of life of urban residents and overall economic development. Therefore, developing effective solutions has become particularly urgent, and this has become a pursuit of many researchers and engineers.

[0003] Intelligent Transportation Systems (ITS) have emerged in this era, combining advanced communication, computer, control, and information technologies to manage and serve traffic intelligently. Their ultimate goal is to reduce traffic congestion, improve road network efficiency, and ensure road safety and sustainability. ITS employs various technologies, such as route guidance strategies, to provide drivers with real-time traffic information and driving suggestions. It aims to achieve a more even distribution of traffic flow to effectively alleviate road congestion.

[0004] However, while ITS offers a promising direction for alleviating traffic problems, a deep understanding and accurate analysis of traffic networks and their dynamic characteristics are essential to truly unlocking its potential advantages. Many existing road network modeling methods can only handle relatively simplified road network structures, making it difficult to fully capture and simulate the complex dynamic changes in traffic flow. More in-depth research typically requires data based on a large number of different road network scenarios, but real-world road network data is both difficult to obtain and expensive, and lacks flexibility.

[0005] It should be noted that the information disclosed in the background section above is only for understanding the background of this application, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0006] To address the challenges of existing technologies in flexibly simulating the complex dynamic changes of traffic flow and the high simulation costs, this invention proposes a method for generating and quantitatively evaluating planar graph networks of varying complexity.

[0007] The technical problem of this invention is solved by the following technical solution:

[0008] A method for generating planar graph networks of varying complexity includes the following steps:

[0009] S1: Determine the boundary of the simulation area based on the traffic scenario and target requirements, and generate a point set within the simulation area;

[0010] S2: Generate a planar graph network with maximum complexity on the point set using the Delaunay triangulation algorithm. The planar graph network with maximum complexity includes edges and all points in the point set. The edges are obtained by connecting the points in the point set.

[0011] S3: Process the planar graph network of maximum complexity based on the edge data information to generate planar graph networks of different complexities.

[0012] In some embodiments, in step S1, the simulated area is a traffic scene, the point set is a collection of traffic elements, the traffic elements are components of urban traffic infrastructure, and the components of urban traffic infrastructure include urban intersections, highway entrances, highway exits, and traffic stations. Generating the point set in the simulated area specifically involves manually specifying or randomly generating a certain number of points in the simulated area. In step S2, the planar network is a road traffic network.

[0013] In some embodiments, in step S2, the planar graph network with the highest complexity conforms to the characteristics of Delaunay triangulation in its topology and cannot have any more edges added without intersecting with other edges.

[0014] In some embodiments, in step S3, the edge data information includes the edge length, the degree of the node, and the edge necessity degree, wherein the edge necessity degree is obtained according to the following formula:

[0015] D = R ÷ L,

[0016] In the formula, D is the necessity degree of the edge, L is the length of the edge, the two endpoints of the edge are a and b, and R is the shortest path length from a to b when the edge has been deleted.

[0017] In some embodiments, step S3, processing the planar graph network of maximum complexity based on the edge data information, includes the following steps: setting basic network condition judgments, then using different strategies for processing, and finally obtaining planar graph networks of different complexities; setting basic network condition judgments includes connectivity judgment, dangling point judgment, and isolated point judgment; wherein, the connectivity judgment is to determine whether the network is connected after deleting the selected edge; the dangling point judgment is to determine whether the degree of the nodes at both ends of the selected edge is equal to one after deleting the selected edge; the isolated point judgment is to determine whether the degree of the nodes at both ends of the selected edge is equal to zero after deleting the selected edge; when deleting the selected edge causes the network connectivity to be destroyed, or when deleting the selected edge causes the degree of the nodes at both ends of the selected edge to be equal to one, or when deleting the selected edge causes the degree of the nodes at both ends of the selected edge to be equal to zero, the basic network condition judgment is in a state of not being satisfied; otherwise, the basic network condition judgment is in a state of being satisfied; when the basic network condition judgment is in a state of not being satisfied, the selected edge is skipped during deletion.

[0018] In some embodiments, the processing using different strategies includes processing the maximum complexity planar graph network based on edge length, processing the maximum complexity planar graph network based on node degree, processing the maximum complexity planar graph network based on both edge length and node degree, and processing the maximum complexity planar graph network based on edge necessity. Processing the maximum complexity planar graph network based on edge length includes the following steps:

[0019] W11: For a constructed planar graph network, calculate the length L of each edge;

[0020] W12: Delete the edge with the largest length L when the basic network condition judgment is satisfied;

[0021] W13: Repeat step W12 until the specified number of edges are deleted;

[0022] Processing the planar graph network with the highest complexity based on the degree of the nodes includes the following steps:

[0023] W21: For a constructed planar graph network, calculate the degree M and N of the two endpoints of each edge;

[0024] W22: Delete the edge with the largest sum of degree M+N between its two endpoints when the basic network condition judgment is satisfied;

[0025] W23: Repeat steps W21 and W22 until the specified number of edges are deleted;

[0026] Processing the maximum complexity planar graph network based on edge length and node degree includes the following steps:

[0027] W31: For a constructed planar graph network, calculate the length L of each edge and the degree M and N of its two endpoints;

[0028] W32: Delete the edge with the largest length L multiplied by the sum of the degrees of the two endpoints M+N when the basic conditions of the network are met, i.e., the edge with the largest L×(M+N);

[0029] W33: Repeat steps W31 and W32 until the specified number of edges are deleted;

[0030] Processing the planar graph network with the highest complexity based on the necessity of edges includes the following steps:

[0031] W41: For a constructed planar graph network, calculate the necessity degree D of each edge;

[0032] W42: Delete the edge with the minimum necessity degree D when the basic conditions of the network are met;

[0033] W43: Repeat steps W41 and W42 until the specified number of edges have been deleted.

[0034] This invention also proposes a quantitative evaluation method for planar graph networks of different complexities, used to perform topological analysis on planar graph networks generated using the above-mentioned methods for generating planar graph networks of different complexities, to perform quantitative comparison and determine their superiority or inferiority, including the following steps:

[0035] A1: Develop at least one criterion for judging the quality of planar graph networks;

[0036] A2: Analyze the topology of the given planar network and perform quantitative analysis based on the judgment criteria in step A1;

[0037] A3: Compare the quantitative analysis results to determine the merits of planar graph networks with different complexities.

[0038] In some embodiments, in step A1, the formulation of at least one criterion for judging the quality of a planar graph network includes a dynamic evaluation method for network quality based on node degree. This dynamic evaluation method for network quality based on node degree includes the following steps:

[0039] B1: The variance of the degree of all nodes in the planar graph network is used as the criterion;

[0040] B2: Starting from the maximum complexity of the planar graph network, process it according to different strategies as described above to gradually reduce the number of edges, and compare the changes in the variance of the degree of all nodes;

[0041] B3: A graph with a rapid and stable decrease in variance is considered relatively uniform and of high quality.

[0042] In some embodiments, in step B3, the graphs in which the variance decreases rapidly and steadily are a series of graphs that gradually reduce complexity using the same strategy.

[0043] The present invention also proposes a computer-readable medium storing a computer program that, when executed by a processor, implements the method described above.

[0044] The beneficial effects of this invention compared to the prior art include:

[0045] This invention uses Delaunay triangulation as the initial step in generating traffic networks, achieving rapid creation of a high-complexity network with the maximum number of edges while ensuring its planarity. By processing the planar network based on the data information of the introduced edges, this invention allows users to dynamically reduce network complexity as needed, generating a series of networks with different complexities, thus providing a more diverse simulation environment and enabling flexible simulation of complex dynamic changes in traffic flow. This invention sets basic network condition judgments during the processing of the planar network, ensuring that a path still exists between any two nodes, guaranteeing network connectivity and usability. This invention does not rely on specific data sources or complex simulation models, and does not require significant resources to run and maintain complex simulation models, solving the technical problem of high simulation costs. Furthermore, this invention can be integrated with traffic flow simulation tools, allowing users to directly perform performance analysis on networks of different complexities, demonstrating good applicability and development prospects.

[0046] Other beneficial effects of the embodiments of the present invention will be further described below. Attached Figure Description

[0047] Figure 1 This is a flowchart illustrating the planar graph network generation method and quantitative evaluation method of different complexities in embodiments of the present invention;

[0048] Figure 2 These are implementation examples of planar graph network generation methods and quantitative evaluation methods of different complexities in this invention.

[0049] Figure 3 This is a flowchart illustrating the method for generating planar graph networks of different complexities in an embodiment of the present invention.

[0050] Figure 4 This is an example diagram of a point set of one hundred points within a simulated area in an embodiment of the present invention;

[0051] Figure 5 This is a schematic diagram showing the result of Delaunay triangulation of the point set in an embodiment of the present invention;

[0052] Figure 6This is a schematic diagram illustrating the result of deleting 20 edges using an edge deletion strategy based on edge length in an embodiment of the present invention.

[0053] Figure 7 This is a schematic diagram showing the result of deleting 60 edges using an edge deletion strategy based on edge length in an embodiment of the present invention;

[0054] Figure 8 This is a schematic diagram showing the result of deleting 107 edges using an edge deletion strategy based on edge length in an embodiment of the present invention;

[0055] Figure 9 This is a schematic diagram illustrating the result of deleting 20 edges using a node degree-based edge deletion strategy in an embodiment of the present invention.

[0056] Figure 10 This is a schematic diagram showing the result of deleting 60 edges using an edge deletion strategy based on node degree in an embodiment of the present invention;

[0057] Figure 11 This is a schematic diagram showing the result of deleting 107 edges using the edge deletion strategy based on node degree in an embodiment of the present invention;

[0058] Figure 12 This is a schematic diagram illustrating the result of deleting 20 edges using an edge deletion strategy based on edge length and node degree in an embodiment of the present invention.

[0059] Figure 13 This is a schematic diagram illustrating the result of deleting 60 edges using an edge deletion strategy based on edge length and node degree in an embodiment of the present invention.

[0060] Figure 14 This is a schematic diagram showing the result of deleting 107 edges using an edge deletion strategy based on edge length and node degree in an embodiment of the present invention.

[0061] Figure 15 This is a schematic diagram showing the result of deleting 20 edges using an edge deletion strategy based on the "necessity" of the edges in an embodiment of the present invention;

[0062] Figure 16 This is the result of deleting 60 edges using an edge deletion strategy based on the "necessity" of the edges in this embodiment of the invention;

[0063] Figure 17 This is the result of deleting 107 edges using an edge deletion strategy based on the "necessity" of the edges in this embodiment of the invention;

[0064] Figure 18 This is a line graph showing the change in degree variance after gradually deleting edges using an edge deletion strategy based on the "necessity" of the edges according to an embodiment of the present invention. Detailed Implementation

[0065] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0066] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0067] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0068] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0069] The present invention will be further described below with reference to the accompanying drawings and preferred embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other.

[0070] It should be noted that the directional terms such as left, right, up, down, top, and bottom used in this embodiment are only relative concepts or are based on the normal use of the product, and should not be considered as restrictive.

[0071] Based on the current state of technological development, road network generation technology is simpler and faster, and can flexibly generate various scenarios to meet different research needs.

[0072] Therefore, developing road network technologies capable of constructing and generating road networks with varying degrees of complexity while maintaining high quality is crucial. This technology not only lays a solid foundation for simulating and analyzing the dynamic characteristics of traffic flow but also provides strong support for implementing and evaluating more efficient and intelligent traffic management strategies, particularly the effectiveness of different route guidance strategies.

[0073] like Figure 1 The diagram shown illustrates the flowcharts of planar graph network generation and quantitative evaluation methods of different complexities in embodiments of the present invention. Figure 2 As shown in the illustration, this invention provides an example of a method for generating and quantitatively evaluating planar graph networks of varying complexity. The method involves several steps: First, a set of points representing traffic intersections or key points is determined, where the set represents a collection of traffic elements. Then, the Delaunay triangulation algorithm is applied to the coordinates of these points to generate a planar graph network with the highest complexity (including the maximum number of edges). Further, a certain number of edges are deleted using different methods to reduce network complexity while maintaining connectivity, thus generating a series of road networks with varying complexities. Finally, the topologies of the road networks constructed using different deletion methods are quantitatively analyzed and compared to determine their superiority. This method provides an efficient way to generate traffic networks of varying complexities and allows for comparison of network quality. This enables decision support for traffic planning at multiple levels.

[0074] like Figure 3 The diagram shows a flowchart illustrating the method for generating planar graph networks of different complexities in an embodiment of the present invention. As can be seen, the steps of the method for generating planar graph networks of different complexities proposed in this embodiment are as follows: S1: Determine the boundary of the simulation area based on the traffic scenario and target requirements, and generate a point set within the simulation area; S2: Generate a planar graph network of maximum complexity on the point set using the Delaunay triangulation algorithm. The maximum complexity planar graph network includes edges and all points in the point set, and the edges are obtained by connecting the points in the point set; S3: Process the maximum complexity planar graph network based on the edge data information to generate planar graph networks of different complexities.

[0075] See Figures 3 to 17 As shown, the specific steps of this embodiment of the invention are as follows:

[0076] 1. For a given set of points, use Delaunay triangulation to generate a network.

[0077] like Figure 4 The diagram shows an example of a point set of one hundred points within a simulated area in an embodiment of the present invention. First, based on the simulated traffic scenario and target requirements, the boundaries of the simulated area and the number of traffic intersections or key points to be identified need to be determined. These identification points can represent various real-world traffic elements; for example, they might be city intersections, highway entrances and exits, or stations. There are two possible methods for creating these point sets representing traffic intersections or key points. The first method is to manually input points or coordinates, directly specifying the location of each traffic intersection or key point. The second method is to use a random algorithm to generate a certain number of points within a preset area. The manual input method is suitable for situations requiring the simulation of specific real-world traffic scenarios, while the random generation method can be used for broader and more general simulation scenarios.

[0078] like Figure 5 The diagram illustrates the result of Delaunay triangulation on a point set in an embodiment of the present invention. It can be seen that generating a planar graph network with maximum complexity through Delaunay triangulation is performed according to the following steps: Before performing Delaunay triangulation, some data structures need to be initialized, including lists or arrays for storing points, edges, and triangles. To begin Delaunay triangulation, a super triangle is first created, which is a sufficiently large triangle to contain all the points. This super triangle is added to the triangle list. The point set created in step one is traversed, and for each point, it is checked whether it lies inside the circumcircle of any triangle in the triangle list. If so, the triangle is removed from the triangle list, and its edges are added to a temporary edge list. For the generated temporary edge list, any duplicate edges are removed. This is because if an edge is a common edge of two triangles, and both triangles are deleted, then this edge should only appear once. New triangles are created using the remaining edges and points, and they are added to the triangle list. After all points have been added, any triangles associated with the super triangle need to be removed from the triangle list. This is because the super triangle is only for initializing the algorithm and is not part of the final triangulation. Finally, the results of the Delaunay triangulation are transformed into a road network. The vertices of the triangles are considered as traffic intersections or key points, and the edges of the triangles are considered as roads.

[0079] Following the steps described above, a road network with maximum complexity is obtained through Delaunay triangulation. This network contains all the points defined in step one and conforms to the properties of Delaunay triangulation in its topology, meaning that no point lies within the circumcircle of any other triangle. Since Delaunay triangulation is a special type of triangulation, it possesses unique properties and characteristics. The network generated by Delaunay triangulation is a planar graph with maximum complexity; the resulting graph is maximally large, meaning that no further edges can be added without intersecting other edges.

[0080] 2. Set basic network conditions, such as maintaining connectivity and eliminating dangling points.

[0081] To determine connectivity, when selecting an edge and considering its deletion, a hypothetical deletion is first performed. Next, the shortest path length between the two endpoints of that edge is calculated. This step can be implemented using Dijkstra's algorithm, the Floyd-Warshall algorithm, or other graph theory algorithms. If the calculated shortest path length is positive infinity, it means that the network's connectivity has been broken after the hypothetical deletion of this edge, and therefore the edge cannot be actually deleted. If the shortest path length is a finite value, it means that the network remains connected after deleting the edge, and the actual deletion operation can be performed.

[0082] Regarding avoiding dangling points (degree 1), when selecting an edge and considering its deletion, it's also necessary to determine the degree of the nodes at both ends of the edge. Specifically, an edge can only be considered for deletion if the degree of both endpoints is greater than 2. Otherwise, deleting the edge would cause one or both nodes to become dangling points (i.e., the point has only one connected edge), in which case the edge cannot be deleted.

[0083] By combining the above methods for determining connectivity and avoiding dangling points, it can be ensured that the network always meets the basic connectivity and structural requirements when generating and modifying road networks of different complexities, thereby ensuring its effectiveness and practicality.

[0084] 3. Gradually remove edges from the network to generate networks of varying complexity.

[0085] Depending on the network generation requirements, four different strategies can be used to gradually remove edges from a planar graph network to generate networks of varying complexity:

[0086] like Figures 6 to 8 The figures shown are schematic diagrams illustrating the results of deleting 20 edges, 60 edges, and 107 edges using the edge deletion strategy based on edge length in an embodiment of the present invention. It can be seen that the preferred approach for processing the planar graph network with the highest complexity based on edge length is an edge deletion strategy based on edge length, with the following steps:

[0087] Edge deletion strategy based on edge length

[0088] W11: Edge Length Calculation: First, the length of each edge in the network needs to be calculated. This can be done using the coordinate information between nodes and the Euclidean distance formula.

[0089] W12: Select the edge to delete: From the calculated edges, select the longest edge for evaluation. This is based on the assumption that a longer path may be considered redundant in some situations.

[0090] It includes a deletion check (i.e., a check to determine the basic network conditions): Before actually deleting an edge, it is necessary to check whether deleting the edge would violate the previously mentioned conditions, such as creating a dangling point or disrupting the network's connectivity. If these conditions are met, the edge can be safely deleted.

[0091] W13: Repeated process: The processes W11 and W12 above need to be repeated continuously until the predetermined number of edges to be deleted is reached or until there are no more edges that meet the conditions.

[0092] like Figures 9 to 11 The figures shown are schematic diagrams illustrating the results of deleting 20 edges, 60 edges, and 107 edges using the edge deletion strategy based on node degree in an embodiment of the present invention. It can be seen that the preferred method for processing the planar graph network with the highest complexity based on node degree is an edge deletion strategy based on node degree, with the following steps:

[0093] Edge deletion strategy based on node degree:

[0094] W21: Degree Calculation: Calculates the degree of the two endpoints of each edge in the network.

[0095] W22: Select edges to delete: From the calculated edges, select the edge with the largest sum of the degrees of its two endpoints for evaluation. This is based on the assumption that edges connecting nodes with high degrees may be redundant in some situations.

[0096] It includes a deletion judgment (i.e., a judgment on setting basic network conditions): similar to the strategy based on edge length, it checks whether the edge can be safely deleted.

[0097] W23: Repeat the process: Continue repeating the steps W21 and W22 above until the predetermined number of edges to be deleted is reached or until no edges meet the conditions. Note that at this point, the degree needs to be recounted because deleting edges will cause the degree to change.

[0098] like Figures 12 to 14 The figures shown are schematic diagrams illustrating the results of deleting 20 edges, 60 edges, and 107 edges using the edge deletion strategy based on edge length and node degree in an embodiment of the present invention. It can be seen that the preferred method for processing the planar graph network with the highest complexity is an edge deletion strategy based on edge length and node degree, with the following steps:

[0099] Edge deletion strategy based on edge length and node degree:

[0100] W31: Degree and Length Calculation: Consider both the length of the side and the degree of its two endpoints.

[0101] W32: Selecting edges to delete: Evaluate the edge with the largest length L multiplied by the sum of the degrees of its two endpoints M+N, i.e., the edge with the largest L×(M+N). This strategy considers both edge length and degree.

[0102] It includes a deletion check (i.e., a check to determine the basic network conditions): it also checks whether it is safe to delete this edge.

[0103] W33: Repeat the process: Continue repeating the processes of W31 and W32 until the predetermined number of edges to be deleted is reached or until no edges meet the conditions. Note that the degree count also needs to be recalculated at this point.

[0104] like Figures 15 to 17 The figures shown are schematic diagrams illustrating the results of deleting 20 edges, 60 edges, and 107 edges using the edge deletion strategy based on edge "necessity" in an embodiment of the present invention. It can be seen that the preferred approach for processing the planar graph network with the highest complexity based on edge necessity is an edge deletion strategy based on edge "necessity," with the following steps:

[0105] Edge deletion strategy based on edge "necessity":

[0106] W41: Calculating "Necessity": For each edge, first assume that the edge has been deleted, then calculate the shortest path length from one endpoint to another. Compare this length R with the original edge length L, i.e., the value of R ÷ L, to obtain the "necessity" of the edge.

[0107] W42: Select the edge to delete: From the calculated edges, select the edge with the lowest "necessity" for evaluation. This is based on the assumption that such an edge is the least necessary.

[0108] It includes a deletion judgment (i.e., a judgment to set the basic conditions of the network): it also checks whether the selected edge can be safely deleted.

[0109] W43: Repeat steps W41 and W42 until the predetermined number of edges to be deleted is reached or until no edges meet the conditions. Note that deleting an edge will cause the "necessity" of other edges to change, so the "necessity" needs to be recalculated.

[0110] In constructing road traffic networks of varying complexity, gradually removing edges is a crucial step. This invention proposes four edge removal methods based on different strategies, each focusing on reducing network complexity while maintaining network connectivity.

[0111] Edge deletion strategies based on edge length focus on removing the longest edges in the network, potentially resulting in a more compact network structure and making them more suitable for scenarios where the goal is to reduce long paths. Edge deletion strategies based on node degree aim to remove edges connecting nodes with high degrees, simplifying highly complex areas such as large transportation hubs. Edge deletion strategies based on both edge length and node degree are a comprehensive approach, considering both edge length and the degree of the connected nodes, aiming to balance the advantages of both strategies and identify potentially redundant long edges connecting nodes with high degrees. Edge deletion strategies based on edge "necessity" consider the potential impact of edge deletion on the entire network. By evaluating the "necessity" of edges, it can identify edges that may be less important in the network, thus more effectively reducing network complexity.

[0112] These four strategies enable the generation of road networks of varying complexity in different scenarios. The choice of strategy depends on the specific application's needs and objectives; however, it is crucial to ensure that network connectivity is not disrupted during the deletion process to avoid generating road networks that do not meet requirements.

[0113] Furthermore, this invention also proposes a quantitative evaluation method for planar graph networks of different complexities. This method is used to perform topological analysis on planar graph networks generated using the aforementioned methods for generating planar graph networks of different complexities, to conduct quantitative comparisons and determine their superiority or inferiority. The steps are as follows:

[0114] A1: Develop at least one criterion for judging the quality of planar graph networks;

[0115] A2: Analyze the topology of the given planar network and perform quantitative analysis based on the judgment criteria in step A1;

[0116] A3: Compare the quantitative analysis results to determine the merits of planar graph networks with different complexities.

[0117] In this embodiment of the invention, topological analysis and quantitative comparison are performed on road networks generated by different strategies and methods. Quantitative analysis is conducted using dynamic methods to compare their advantages and disadvantages. For example... Figure 18 The figure shows a line graph illustrating the change in degree variance after progressively deleting edges using an edge deletion strategy based on the "necessity" of the edges in this embodiment of the invention. As can be seen, the dynamic evaluation is as follows:

[0118] Dynamic evaluation: Network performance evaluation based on node degree

[0119] Dynamic evaluation focuses on the trend of changes in the topology of the entire network as the number of edges gradually decreases.

[0120] B1: Judgment Criteria Setting: Common traffic network nodes are typically 4 degrees, but there are also nodes with 3 or 5 degrees. Considering this uniformity, the variance of node degree is chosen as the evaluation index. The smaller the variance, the more uniform the node degree in the network. The variance of the degree of all nodes in the planar network is used as the judgment criterion.

[0121] B2: Analysis process: Start with the network in the initial state (i.e., maximum complexity); gradually delete edges according to the preset strategy; after each edge deletion, calculate the variance of the node degree of the current network; record and analyze the trend of variance changes.

[0122] B3: Evaluation Criteria: A rapid and stable decrease in variance is considered as a rapid and stable convergence of the network structure to a uniform state. Such networks are considered to be of high quality. That is, a series of graphs whose complexity is gradually reduced using the same strategy are considered to be relatively uniform and of high quality if the variance of the series of graphs decreases rapidly and stably.

[0123] This invention provides a systematic and flexible method for generating traffic road networks of varying complexities and their quantitative evaluation for traffic flow simulation and research. This invention offers solutions to several key issues in the field of traffic network research and simulation:

[0124] 1. Addressing the lack of flexibility in existing network generation technologies:

[0125] In existing traffic network simulation tools, users are typically limited to using predefined networks or manually building networks, which is time-consuming and inflexible. The method described in this invention enables users to quickly generate a series of networks with varying complexities, significantly improving flexibility and efficiency.

[0126] 2. Addressing the lack of diversity in existing simulation environments:

[0127] To conduct comprehensive traffic flow studies, testing is required in various network environments. The dynamic complexity control and optional modules of this invention enable the creation of diverse networks, allowing for more comprehensive analysis.

[0128] 3. Solve the problem of low computational efficiency in existing technologies:

[0129] For large-scale transportation networks, generation and simulation typically require significant computational resources. This invention improves computational efficiency by using an efficient network generation method based on Delaunay triangulation, progressively reducing complexity while maintaining connectivity.

[0130] 4. Addressing the lack of transportation planning and policy evaluation in existing technologies:

[0131] Transportation planners and government agencies need tools to evaluate different transportation network designs and policies. Embodiments of this invention provide a flexible and practical method that enables them to simulate and analyze traffic flows across various network configurations, thereby allowing for more informed decision-making.

[0132] Furthermore, the embodiments of the present invention also have the following advantages:

[0133] 1. Geometry-driven approach: Unlike traditional methods based on existing data or simulation, the embodiments of the present invention allow for more natural and flexible network generation, especially suitable for new or poorly planned areas.

[0134] 2. Adjustment of Network Complexity: Embodiments of this invention allow users to adjust the complexity of the network as needed. This flexibility enables the invention to adapt to projects of various sizes and requirements, without being limited to specific datasets or models.

[0135] 3. Versatility and Adaptability: Because the embodiments of this invention employ a geometry-based method, it can be widely applied to various fields, not only transportation planning, but also urban planning, network optimization, and communications. This versatility gives it broad application potential in the market.

[0136] 4. Low cost: Since the embodiments of the present invention do not rely on specific data sources or complex simulation models, they may have advantages in terms of resources and cost. Users do not need to purchase licensed, expensive datasets, nor do they need to invest significant resources in running and maintaining complex simulation models.

[0137] 5. High efficiency: Geometry-based methods are more computationally efficient.

[0138] 6. Market Gap: In the field of road network generation, many existing methods and products typically focus on using existing data and complex simulations. This invention provides a novel, geometry-based method that fills a market gap, offering a solution for projects requiring rapid, flexible, and low-cost network generation.

[0139] The above description provides a further detailed explanation of the present invention in conjunction with specific / preferred embodiments, and it should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various substitutions or modifications can be made to these described embodiments without departing from the concept of the present invention, and all such substitutions or modifications should be considered within the scope of protection of the present invention. In the description of this specification, the reference to terms such as "an embodiment," "some embodiments," "preferred embodiment," "example," "specific example," or "some examples," etc., indicates that the specific features, structures, materials, or characteristics described in connection with that embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described can be combined in any suitable manner in one or more embodiments or examples. Without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification and the features of different embodiments or examples. Although the embodiments of the present invention and their advantages have been described in detail, it should be understood that various changes, substitutions, and modifications can be made herein without departing from the scope of protection of the patent application.

Claims

1. A method for generating planar graph networks of varying complexity, characterized in that, Includes the following steps: S1: Determine the boundary of the simulation area based on the traffic scenario and target requirements, and generate a point set within the simulation area; S2: Generate a planar graph network with maximum complexity on the point set using the Delaunay triangulation algorithm. The planar graph network with maximum complexity includes edges and all points in the point set. The edges are obtained by connecting the points in the point set. S3: Process the planar graph network of maximum complexity based on the edge data information to generate planar graph networks of different complexities; In step S3, processing the planar graph network with the highest complexity based on the edge data information includes the following steps: setting basic network condition judgments, then using different strategies for processing, and finally obtaining planar graph networks with different complexities; setting basic network condition judgments includes connectivity judgment, dangling point judgment, and isolated point judgment; wherein, the connectivity judgment is to determine whether the network is connected after deleting the selected edge; the dangling point judgment is to determine whether the degree of the nodes at both ends of the selected edge is equal to one after deleting the selected edge; the isolated point judgment is to determine whether the degree of the nodes at both ends of the selected edge is equal to zero after deleting the selected edge; when deleting the selected edge causes the network connectivity to be destroyed, or causes the degree of the nodes at both ends of the selected edge to be equal to one, or causes the degree of the nodes at both ends of the selected edge to be equal to zero, the basic network condition judgment is in a state of not being satisfied; otherwise, the basic network condition judgment is in a state of being satisfied; when the basic network condition judgment is in a state of not being satisfied, the selected edge is skipped during deletion; The different processing strategies include processing the maximum complexity planar graph network based on edge length, processing the maximum complexity planar graph network based on node degree, processing the maximum complexity planar graph network based on both edge length and node degree, and processing the maximum complexity planar graph network based on edge necessity. Processing the maximum complexity planar graph network based on edge length includes the following steps: W11: For a constructed planar graph network, calculate the length L of each edge; W12: Delete the edge with the largest length L when the basic conditions of the network are met; W13: Repeat step W12 until the specified number of edges are deleted; Processing the planar graph network with the highest complexity based on the degree of the nodes includes the following steps: W21: For a constructed planar graph network, calculate the degree M and N of the two endpoints of each edge; W22: Delete the edge with the largest sum of degree M+N between its two endpoints when the basic network condition judgment is satisfied; W23: Repeat steps W21 and W22 until the specified number of edges are deleted; Processing the planar graph network with the highest complexity based on the edge length and node degree includes the following steps: W31: For a constructed planar graph network, calculate the length L of each edge and the degree M and N of its two endpoints; W32: Delete the edge with the largest length L multiplied by the sum of the degrees of the two endpoints M+N when the basic conditions of the network are met, i.e., the edge with the largest L×(M+N); W33: Repeat steps W31 and W32 until the specified number of edges are deleted; Processing the planar graph network with the highest complexity based on the necessity of edges includes the following steps: W41: For a constructed planar graph network, calculate the necessity degree D of each edge; W42: Delete the edge with the minimum necessity degree D when the basic conditions of the network are met; W43: Repeat steps W41 and W42 until the specified number of edges have been deleted.

2. The method for generating planar graph networks of different complexities as described in claim 1, characterized in that, In step S1, the simulated area is a traffic scenario, the point set is a collection of traffic elements, the traffic elements are components of urban traffic infrastructure, and the components of urban traffic infrastructure include urban intersections, highway entrances, highway exits, and traffic stations. Generating the point set in the simulated area specifically involves manually specifying or randomly generating a certain number of points in the simulated area. In step S2, the planar network is a road traffic network.

3. The method for generating planar graph networks of different complexities as described in claim 1, characterized in that, In step S2, the planar graph network with the highest complexity conforms to the characteristics of Delaunay triangulation in terms of topology and cannot have any more edges added without intersecting with other edges.

4. The method for generating planar graph networks of different complexities as described in claim 1, characterized in that, In step S3, the edge data information includes the edge length, the degree of the node, and the edge necessity degree, wherein the edge necessity degree is calculated according to the following formula: In the formula, D is the necessity degree of the edge, L is the length of the edge, the two endpoints of the edge are a and b, and R is the shortest path length from a to b when the edge has been deleted.

5. A quantitative evaluation method for planar graph networks of varying complexity, characterized in that, The method for performing topological analysis, quantitative comparison, and evaluation of planar graph networks generated using the method for generating planar graph networks of different complexities as described in claim 1 includes the following steps: A1: Develop at least one criterion for judging the quality of planar graph networks; A2: Analyze the topology of the given planar network and perform quantitative analysis based on the judgment criteria in step A1; A3: Compare the quantitative analysis results to determine the merits of planar graph networks with different complexities.

6. The quantitative evaluation method for planar graph networks of different complexities as described in claim 5, characterized in that, In step A1, the formulation of at least one criterion for judging the quality of planar graph networks includes a dynamic evaluation method for network quality based on node degree. This dynamic evaluation method for network quality based on node degree includes the following steps: B1: The variance of the degree of all nodes in the planar graph network is used as the criterion; B2: Starting from the maximum complexity of the planar graph network, different strategies are used to gradually reduce the number of edges, and the changes in the variance of the degree of all nodes are compared. B3: A graph with a rapid and stable decrease in variance is considered relatively uniform and of high quality.

7. The quantitative evaluation method for planar graph networks of different complexities as described in claim 6, characterized in that, In step B3, the graphs in which the variance decreases rapidly and steadily are a series of graphs that gradually reduce complexity using the same strategy.

8. A computer-readable medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the method as described in claims 1-7.

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