Layered route network construction method under complex urban low-altitude environment
By employing a hierarchical airway network construction method, which combines visualization and backbone network generation with edge optimization, the problem of insufficient path efficiency and redundancy in complex urban low-altitude environments is solved. This achieves safe and efficient low-altitude airway network construction, improving the controllability of urban low-altitude traffic operations and airspace utilization efficiency.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- NANJING UNIVERSITY OF AERONAUTICS & ASTRONAUTICS SHENZHEN RESEARCH INSTITUTE
- Filing Date
- 2026-04-30
- Publication Date
- 2026-07-14
Smart Images
Figure CN122392367A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of low-altitude airway construction technology, specifically relating to a method for constructing a layered airway network in a complex urban low-altitude environment. Background Technology
[0002] With the continuous development and utilization of urban low-altitude airspace, the application of drones in scenarios such as logistics delivery, emergency rescue, and inspection and monitoring continues to expand. Compared with traditional ground transportation, low-altitude drones have advantages such as flexible paths, fast response speed, and relatively low deployment costs. However, their operating space is concentrated in urban low-altitude areas with dense buildings and significant obstacle constraints, thus facing higher airspace organization complexity and operational safety pressures in the process of large-scale application.
[0003] Most existing research on low-altitude airway network construction first generates complete candidate airway paths, and then selects the segments to be retained from the candidate paths to form a low-altitude airway network. This takes into account the sparsity problem of the airway network. However, it does not fully consider the redundancy and efficiency of different OD pairs for intermediate airway network paths. A good consensus has not yet been formed in terms of network size control, path efficiency improvement and path structure redundancy.
[0004] In complex urban low-altitude environments, available airspace is limited. To ensure safe operation, it is necessary to reduce operational complexity and control the scale of the low-altitude airway network. However, methods such as minimum spanning tree to generate sparse airway networks may have insufficient path efficiency and redundancy between different origin-destination (OD) pairs. Therefore, there is an urgent need for a low-altitude airway network construction method that can both consider the sparsity of the low-altitude airway network and improve the path efficiency and redundancy between different OD pairs. Summary of the Invention
[0005] The purpose of this invention is to provide a method for constructing a hierarchical airway network in a complex urban low-altitude environment.
[0006] This application provides a method for constructing a hierarchical airway network in a complex urban low-altitude environment, characterized by comprising: Hierarchical candidate networks are constructed using the visualization method; Layered multiple OD paths are superimposed to form a layered airway network; Backbone network generation; By supplementing the edges, an augmented and optimized network is formed.
[0007] In one embodiment of this application, constructing a hierarchical candidate network using a visual method includes: Select a set of sampling points in free space that can describe the accessibility potential of obstacle edges and open areas; Candidate edges are established based on the principle of visibility; Transform a continuous flyable space into a computable graph structure.
[0008] In one embodiment of this application, the sampling points include the first... Layer free space The system incorporates two types of sampling points: one type consists of obstacle boundary sampling points, used to characterize obstacle avoidance paths; the other type consists of free space sampling points, used to maintain basic connectivity within open areas. The union of these two types of points is denoted as the first... Layer node set .
[0009] In one embodiment of this application, establishing candidate edges based on the visibility principle includes: If node The connection is completely located Within, and the distance between nodes does not exceed the preset edge connection threshold. Then, a candidate edge is established between the two points, i.e. Therefore, we obtain the first... Layered View .
[0010] In one embodiment of this application, the transformation of a continuous flyable space into a computable graph structure includes: By combining the candidate images of each height layer with the necessary inter-layer transformation edges, a complete layered visual image is formed. ;as well as Assign a comprehensive cost to candidate edges: Define the edge The length is The average risk is After normalization, the comprehensive edge weight is defined as: in, This is the trade-off coefficient between the length term and the risk term.
[0011] In one embodiment of this application, the layered multi-OD path superposition to form a layered route network includes: connecting OD points to the candidate network, for any OD pair The complete diagram after connection The search engine searches for its main path and low-overlap alternative paths; among which... Set path The set of edges on is The total path cost is defined as follows: Therefore, the main path is defined as in, Let i be the set of feasible paths connecting i and j; and Define path and The overlap rate in, Indicates the path length; When the overlap rate between the new path and the retained path does not exceed a preset threshold When necessary, keep it as an alternative path; The shared structure of the path set is extracted, which involves identifying repeatedly shared edges, intersection nodes, and main passageways among different origin-destination (OD) paths. Through path filtering and spatial aggregation, the path set is transformed into a multi-OD path network with shared structure characteristics. .
[0012] In one embodiment of this application, the backbone network generation adopts a minimum spanning tree-based backbone network generation method, which extracts flight segments covering all take-off and landing points with relatively low total cost from the multi-OD path network to form an initial backbone network. ;in Let the minimum spanning tree be Then its objective is The above formula indicates that, under the condition of ensuring connectivity of all take-off and landing points, priority is given to retaining the main flight segments with lower overall costs; It is a picture Spanning tree, It is the weight of the edge connecting i and j.
[0013] In one embodiment of this application, the edge-padding optimization to form an augmented optimization network includes: Perform efficiency edge supplementation to form an efficiency edge supplementation set. ; Perform redundant edge padding to form a set of redundant enhanced edge padding. ;as well as By combining the initial backbone edges, efficiency-added edges, and redundancy-added edges, the final hierarchical route network can be obtained. : .
[0014] In one embodiment of this application, the efficiency-based edge compensation includes: Define key OD pairs The detour coefficient is in, Represents the initial backbone network The optimal path cost connecting i and j. express The optimal path cost connecting i and j; when When the value is close to 1, it indicates that the optimal travel path in the backbone is not significantly different from the original optimal path; when... Exceeding the preset threshold When this occurs, it indicates that the path of the OD pair in the initial backbone network has detoured. The main path is then added back to the backbone network to form an efficiency-added edge set. This is to reduce unnecessary local detours and improve network accessibility.
[0015] In one embodiment of this application, the redundant edge padding includes: For each OD pair in the OD pair set K, check whether it has an overlap rate with the main path in the current network that exceeds a preset threshold. Alternative paths are selected; if they exist, paths with lower costs and satisfying overlap rate constraints are chosen from the candidate path set to supplement the network, forming a redundant enhanced edge supplementation set. .
[0016] The beneficial effects of this invention are: Compared to existing technologies, this invention addresses complex urban low-altitude obstacle environments by combining hierarchical flyable network construction with multi-OD path-driven modeling. This transforms the airway network from a "spatially feasible" to a "demand-driven" approach, significantly improving the network's adaptability to actual transportation needs while ensuring flight safety. Furthermore, through backbone network extraction and edge optimization, network redundancy and structural complexity are effectively reduced, while balancing connectivity and path efficiency, thus enhancing the controllability and overall performance of low-altitude traffic operations. In addition, the hierarchical airway structure helps alleviate airspace congestion and improve airspace utilization efficiency, giving the constructed airway network good structural characteristics and scalability, providing a safe and efficient foundation for urban low-altitude traffic operations.
[0017] Other features and advantages of the invention will be set forth in the following description, and will be apparent in part from the description, or may be learned by practicing the invention. The objects and other advantages of the invention are realized and obtained through the structures particularly pointed out in the description and the drawings.
[0018] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, preferred embodiments are described below in detail with reference to the accompanying drawings. Attached Figure Description
[0019] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.
[0020] Figure 1This is a flowchart illustrating a preferred embodiment of the method for constructing a layered airway network in a complex urban low-altitude environment according to the present invention. Figure 2 This is a hierarchical candidate network diagram of a preferred embodiment of the present invention; Figure 3 This is an initial backbone low-altitude airway network according to a preferred embodiment of the present invention; Figure 4 This is a schematic diagram of OD pair efficiency padding according to a preferred embodiment of the present invention; Figure 5 This is a schematic diagram of OD pair redundancy patching according to a preferred embodiment of the present invention; Figure 6 This is an augmented low-altitude airway network, a preferred embodiment of the present invention. Detailed Implementation
[0021] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0022] This application provides a method for constructing a hierarchical airway network in a complex urban low-altitude environment, which will be described in detail below. It should be noted that the order of description of the following embodiments is not intended to limit the preferred order of the embodiments of this application. Furthermore, the descriptions of each embodiment have their own emphasis; parts not described in detail in a certain embodiment can be referred to in the relevant descriptions of other embodiments.
[0023] See Figure 1 One embodiment of this application provides a method for constructing a hierarchical airway network in a complex urban low-altitude environment, including: Hierarchical candidate networks are constructed using the visualization method; Layered multiple OD paths are superimposed to form a layered airway network; Backbone network generation; By supplementing the edges, an augmented and optimized network is formed.
[0024] In this implementation, a visual graph method is used to construct a hierarchical candidate network. The core idea is to select a set of sampling points in free space that can describe the accessibility potential of obstacle edges and open areas, and then establish candidate connections based on the visibility principle. This transforms the continuous flyable space into a computable graph structure, providing a foundation for subsequent multi-OD path search and backbone network generation.
[0025] Specifically, the sampling points include the first... Layer free space The system incorporates two types of sampling points: one type consists of obstacle boundary sampling points, used to characterize obstacle avoidance paths; the other type consists of free space sampling points, used to maintain basic connectivity within open areas. The union of these two types of points is denoted as the first... Layer node set .
[0026] The establishment of candidate edges based on the visibility principle includes: If node The connection is completely located Within, and the distance between nodes does not exceed the preset edge connection threshold. Then, a candidate edge is established between the two points, i.e. Therefore, we obtain the first... Layered View .
[0027] The process of transforming a continuous flyable space into a computable graph structure includes: By combining the candidate images of each height layer with the necessary inter-layer transformation edges, a complete layered visual image is formed. ;as well as To balance flight efficiency and risk exposure, a comprehensive cost can be assigned to candidate edges: [Edge designation] The length is The average risk is After normalization, the comprehensive edge weight is defined as: in, This is the trade-off coefficient between the length term and the risk term.
[0028] At this point, the continuous low-altitude airspace has been transformed into a hierarchical network graph structure that is flyable, searchable, and weighted, serving as the basis for the next step of multi-OD path generation.
[0029] For example, in one embodiment, the effective obstacle areas for each height layer are first determined based on the building outline, height information, and vertical safety interval, and sampling points are set within the obstacle boundaries and free space. Then, candidate edges are generated based on the visibility principle that node connections do not traverse the effective obstacles of the current layer and satisfy the edge distance constraint. Thus, taking 10 m, 20 m, 30 m, 40 m, and 50 m height layers as examples, hierarchical candidate networks are obtained respectively, providing a basic graph structure for subsequent OD point access, multi-OD path search, and backbone network extraction. See also... Figure 2The diagram shows a hierarchical candidate network generated in one embodiment. It illustrates candidate flyable networks formed at different height levels, with variations in the distribution of effective obstacles and the range of flyable space at each level. Specifically, at lower height levels, the flyable space is more obstructed due to building height and safety interval constraints, and candidate connections mainly extend along obstacle boundaries and locally open areas. As the height increases, some low-rise buildings no longer constitute effective obstacles at the current height level, the flyable space becomes more open overall, and the spatial distribution and connectivity of the candidate network change accordingly.
[0030] Furthermore, in this embodiment, the layered multi-OD path superposition to form a layered route network includes: connecting OD points to the candidate network, for any OD pair The complete diagram after connection The search engine searches for its main path and low-overlap alternative paths; among which... Set path The set of edges on is The total path cost is defined as follows: Therefore, the main path is defined as in, Let i be the set of feasible paths connecting i and j; and Define path and The overlap rate in, Indicates the path length; When the overlap rate between the new path and the retained path does not exceed a preset threshold When necessary, keep it as an alternative path; Since representative paths of multiple OD sets often have repeated edges, adjacent corridors, and intersections in space, to avoid the path results merely representing a simple superposition of a large number of discrete paths, a shared structure extraction is performed on the path set. This involves identifying repeatedly shared edges, intersection nodes, and main passageways between different OD paths, and then transforming them into a multi-OD path network with shared structural characteristics through path filtering and spatial aggregation. This network reflects the spatial distribution of major passageways and serves as a direct input for generating the backbone network.
[0031] Furthermore, although the multi-OD path network has aggregated the spatial distribution of major takeoff and landing OD pairs, it still contains many repetitive segments and local redundancy, making it difficult to directly serve as a hierarchically clear route backbone. Therefore, the backbone network generation adopts a minimum spanning tree-based backbone network generation method, extracting segments from the multi-OD path network that cover all takeoff and landing points and have a relatively low total cost to form the initial backbone network. The purpose of this approach is to compress the originally dense path network into a simple, globally connected backbone framework, providing a foundation for subsequent edge-filling optimization. This approach corresponds to the basic principle of the spanning tree derivation method, which first forms a minimal spanning tree to create a simplified backbone, and then improves detour and redundancy performance through subsequent edge-filling.
[0032] Specifically, let the minimum spanning tree be... Then its objective is The above formula indicates that, under the condition of ensuring connectivity of all take-off and landing points, priority is given to retaining the main road sections with lower overall costs; T is the graph. Spanning tree, This is the weight of the edge connecting i and j. The result of the minimum spanning tree is a set of paths that cover all origin and destination points and have a small total cost. It completes the first large-scale sparsification of the multi-OD path network, resulting in the initial backbone network B. 0 .
[0033] For example, in one embodiment, firstly, the main path and alternative paths for multiple OD pairs are searched based on the candidate network, and different OD paths are superimposed to form a multi-OD path network; then, taking the take-off and landing points as the associated objects, the comprehensive cost of the main paths of each key OD pair is used as the weight to construct a weighted association graph of take-off and landing points; finally, the minimum spanning tree method is used to extract the main segments that cover all take-off and landing points and have the smallest total cost, and the associated edges in the spanning tree are mapped back to the corresponding underlying routes to form... Figure 3 The initial backbone low-altitude airway network is shown. This network achieves overall connectivity and scale control, but due to the uniqueness of the tree-structured paths, local detours and redundancy issues may still exist, thus requiring further edge-filling optimization. See also... Figure 3 This figure illustrates an initial backbone low-altitude airway network as an example. The diagram shows the backbone airway structure obtained by further sparsifying the multi-OD path network. This network retains the main transit paths connecting each takeoff and landing point and forms a connected skeleton covering all takeoff and landing points. Compared to the original multi-OD path network, the initial backbone network has a significantly reduced number of air segments, a simpler network structure, and better reflects the main corridors and key connections in the low-altitude airway network.
[0034] Furthermore, while minimum spanning trees guarantee global connectivity and a simple backbone, the tree structure only provides a single path. Some critical origin-destination (OD) paths within the backbone may deviate from the original main path, resulting in significant local detours. Additionally, some critical OD pairs lack alternative paths, leading to weak network robustness once local edges fail. Therefore, targeted edge patching is needed on the backbone network to form a more suitable augmented optimization network.
[0035] In this embodiment, the edge-padding optimization to form an augmented optimization network includes: Perform efficiency edge supplementation to form an efficiency edge supplementation set. ; Perform redundant edge padding to form a set of redundant enhanced edge padding. ;as well as By combining the initial backbone edges, efficiency-added edges, and redundancy-added edges, the final hierarchical route network can be obtained. : .
[0036] The efficiency-based edge compensation includes: Define key OD pairs The detour coefficient is in, Represents the initial backbone network Middle connection and The optimal path cost, express Middle connection and The optimal path cost; when When the value is close to 1, it indicates that the optimal travel path in the backbone is not significantly different from the original optimal path; when... Exceeding the preset threshold When this occurs, it indicates that the path of the OD pair in the initial backbone network has detoured. The main path is then added back to the backbone network to form an efficiency-added edge set. This is to reduce unnecessary local detours and improve network accessibility.
[0037] For example, in one embodiment, the optimal path cost of a critical OD pair in the initial backbone network is first calculated and compared with its main path cost in the original candidate path network to obtain a detour coefficient. When the detour coefficient exceeds a preset threshold, the OD pair is determined to have a significant efficiency loss. Subsequently, necessary segments in the main path of the OD pair that are not yet included in the initial backbone network are added back to the backbone network, forming an efficiency-added edge set. The efficiency-added edges obtained in this way do not regenerate the complete network, but rather, while maintaining the simplicity of the backbone network, perform targeted corrections for critical OD pairs with large local detours. See also Figure 4This diagram illustrates the efficiency-enhancing edge supplementation for OD pairs in one embodiment. Taking a key OD pair as an example, the diagram compares the difference between the path of this OD pair in the initial backbone network and its main path in the original multi-OD path network. Red represents the path in the initial backbone network, and blue represents the more efficient path added to the original OD path network. After the initial backbone network extracts the backbone paths, some OD pairs may need to detour along the backbone structure, resulting in a significantly longer path in the backbone path compared to the original main path. The added efficiency segments in the diagram are used to reduce the detour degree of this OD pair in the backbone network.
[0038] The redundant edge padding includes: For each OD pair in the OD pair set K, check whether it has an overlap rate with the main path in the current network that does not exceed a preset threshold. If no alternative path exists, a path with lower cost and satisfying the overlap rate constraint is selected from the candidate path set to supplement the network, forming a redundant enhanced edge supplementation set. .
[0039] For example, in one embodiment, for each OD pair in the critical OD set, it is first checked whether there is an alternative path in the current network that satisfies the overlap rate constraint. If there is a lack of low-overlap candidate paths in the current network, paths with lower costs and an overlap rate with the main path not exceeding a preset threshold are selected from the candidate path set retained in the aforementioned multi-OD path search phase. Segments not yet included in the current network are then added to these paths to form a redundant enhanced edge set. This process can improve the dual-path reachability of critical OD pairs and the network's resilience to disturbances without significantly increasing the network size. See also Figure 5 This diagram illustrates redundant edge supplementation for an OD pair as an example. Taking a critical OD pair as an example, the diagram shows the process of adding a low-overlap alternative path outside the existing main travel path. Red represents the travel path in the initial backbone network, and blue represents the added low-overlap alternative path. Unlike efficiency edge supplementation, which is mainly used to shorten detours, the purpose of redundant edge supplementation is to provide critical OD pairs with backup travel paths that have a low degree of spatial overlap with the main path, ensuring that the OD pair still has an alternative travel path when local segments are blocked or fail.
[0040] See Figure 6 This is a schematic diagram of an augmented low-altitude airway network according to one embodiment. The diagram shows the final hierarchical airway network formed after integrating efficiency-based and redundancy-based edge additions on top of the initial backbone network. Compared to... Figure 3 The initial backbone network shown retains the characteristics of a clear main structure and a controlled number of flight segments. At the same time, for some OD pairs, more efficient routes have been added to reduce detours and routes to provide redundancy for backup routes, thus improving the network's path efficiency and structural resilience.
[0041] In this embodiment, an initial backbone network is first obtained using the minimum spanning tree method. Then, for critical OD pairs with detour coefficients exceeding a threshold, necessary segments from the corresponding main path are added to form an efficiency-based edge set. Further, for critical OD pairs lacking low-overlap alternative paths, alternative path segments satisfying overlap rate constraints are added to form a redundant edge set. Finally, the initial backbone edges, efficiency-based edges, and redundant edges are merged to obtain the desired network. Figure 6 The augmented low-altitude airway network shown is an example of such a network. This network balances airway network sparsity, OD traffic efficiency, and redundancy of key OD pairs, and can serve as a basic airway structure for organizing UAV operations in complex urban low-altitude environments.
[0042] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.
Claims
1. A method for constructing a hierarchical airway network in a complex urban low-altitude environment, characterized in that, include: Hierarchical candidate networks are constructed using the visualization method; Layered multiple OD paths are superimposed to form a layered airway network; Backbone network generation; By supplementing the edges, an augmented and optimized network is formed.
2. The hierarchical route network construction method according to claim 1, characterized in that, The construction of the hierarchical candidate network using the visual graph method includes: Select a set of sampling points in free space that can describe the accessibility potential of obstacle edges and open areas; Candidate edges are established based on the principle of visibility; Transform a continuous flyable space into a computable graph structure.
3. The hierarchical route network construction method according to claim 2, characterized in that, The sampling points include those in the first... Layer free space The system incorporates two types of sampling points: one type consists of obstacle boundary sampling points, used to characterize obstacle avoidance paths; the other type consists of free space sampling points, used to maintain basic connectivity within open areas. The union of these two types of points is denoted as the first... Layer node set .
4. The hierarchical route network construction method according to claim 3, characterized in that, The establishment of candidate edges based on the visibility principle includes: If node The connection is completely located Within, and the distance between nodes does not exceed the preset edge connection threshold. Then, a candidate edge is established between the two points, i.e. Therefore, we obtain the first... Layered View .
5. The hierarchical route network construction method according to claim 3, characterized in that, The process of transforming a continuous flyable space into a computable graph structure includes: By combining the candidate images of each height layer with the necessary inter-layer transformation edges, a complete layered visual image is formed. ;as well as Assign a comprehensive cost to candidate edges: Define the edge The length is The average risk is After normalization, the comprehensive edge weight is defined as: in, This is the trade-off coefficient between the length term and the risk term.
6. The hierarchical route network construction method according to claim 5, characterized in that, The layered multi-OD path superposition to form a layered route network includes: connecting OD points to the candidate network, and for any OD pair... The complete diagram after connection The search engine searches for its main path and low-overlap alternative paths; among which... Set path The set of edges on is The total path cost is defined as follows: Therefore, the main path is defined as in, Let i be the set of feasible paths connecting i and j; and Define path and The overlap rate in, Indicates the path length; When the overlap rate between the new path and the retained path does not exceed a preset threshold When necessary, keep it as an alternative path; The shared structure of the path set is extracted, which involves identifying repeatedly shared edges, intersection nodes, and main passageways among different origin-destination (OD) paths. Through path filtering and spatial aggregation, the path set is transformed into a multi-OD path network with shared structure characteristics. .
7. The hierarchical route network construction method according to claim 6, characterized in that, The backbone network generation adopts a minimum spanning tree-based backbone network generation method, which extracts flight segments that cover all takeoff and landing points and have a relatively small total cost from the multi-OD path network to form the initial backbone network. ;in Let the minimum spanning tree be Then its objective is The above formula indicates that, under the condition of ensuring connectivity of all take-off and landing points, priority is given to retaining the main road sections with lower overall costs; T is the graph. Spanning tree, yes The weight of the edge connecting j.
8. The hierarchical route network construction method according to claim 7, characterized in that, The edge-filling optimization, forming an augmented optimization network, includes: Perform efficiency edge supplementation to form an efficiency edge supplementation set. ; Perform redundant edge padding to form a set of redundant enhanced edge padding. ;as well as By combining the initial backbone edges, efficiency-added edges, and redundancy-added edges, the final hierarchical route network can be obtained. : .
9. The hierarchical route network construction method according to claim 8, characterized in that, The efficiency-based edge compensation includes: Define key OD pairs The detour coefficient is in, Represents the initial backbone network Middle connection The optimal path cost of j express Middle connection The optimal path cost with respect to j; when When the value is close to 1, it indicates that the optimal travel path in the backbone is not significantly different from the original optimal path; when... Exceeding the preset threshold When this occurs, it indicates that the path of the OD pair in the initial backbone network has detoured. The main path is then added back to the backbone network to form an efficiency-added edge set. This is to reduce unnecessary local detours and improve network accessibility.
10. The hierarchical route network construction method according to claim 8, characterized in that, The redundant edge padding includes: For each OD pair in the OD pair set K, check whether it has an overlap rate with the main path in the current network that exceeds a preset threshold. Alternative paths are selected; if they exist, paths with lower costs and satisfying overlap rate constraints are chosen from the candidate path set to supplement the network, forming a redundant enhanced edge supplementation set. .