Design method of survivability communication network

Abstract

The invention relates to a design method of an survivability communication network, and belongs to the technical field of communication network design methods. In order to overcome the defect of poor survivability of the communication network with the shortest laid line in the prior art, the method comprises the following steps: 1, establishing a minimum spanning tree model and obtaining the shortest communication network: selecting n communication cities as nodes of the wired communication network, establishing an approximate complete empowerment graph # imgabs0 #, solving a minimum spanning tree # imgabs2 # of the n nodes on the graph # imgabs1 #, calculating a minimum spanning tree # imgabs3 #, and establishing a minimum spanning tree model; obtaining a communication network which is connected with the shortest total line of the n communication cities; 2, determining important network nodes: determining leaf nodes and important nodes in the shortest communication network constructed by the n nodes established in the step 1; 3, aiming at the important nodes obtained in the step 2, carrying out line optimization on the communication network in the step 1; and 4, establishing a damaged network repair model. According to the method, the survivability of the constructed network is improved, and the cost is reduced.

Description

Technical Field

[0001] The invention relates to a design method for a destruction-resistant communication network, and belongs to the technical field of communication network design methods. Background Art

[0002] Communication networks are currently indispensable to social development, which determines the timeliness of information communication in the entire society. Communication networks are set up between cities and countries. In order to pursue high speed, the laying cost is relatively high. In order to reduce costs, the general method is to shorten the laying line, but this method of communication network is easily damaged, and the cost of repairing after damage is high and time-consuming and labor-intensive. Summary of the invention

[0003] The purpose of the present invention is to solve the problem of poor anti-destruction performance of the communication network with the shortest laying line in the prior art, and to provide a design method for a communication network with high anti-destruction performance.

[0004] In order to solve the above problems, the present application is implemented through the following technical solutions: A method for designing a survivable communication network is characterized in that it comprises the following steps: 1. Establish a minimum spanning tree model to obtain the shortest communication network: select n communication cities as nodes of the wired communication network and establish an approximate fully weighted graph , in Figure Find the minimum spanning tree of n nodes , calculate the minimum spanning tree , obtain the communication network with the shortest total line connecting n communication cities; 2. Determine the important nodes of the network: In the communication network with the shortest total line constructed by the n nodes established in step 1, determine the leaf nodes and important nodes; 3. Optimize the communication network in step 1 for the important nodes obtained in step 2; 4. Establish a damaged network repair model.

[0005] Preferably, the approximate fully weighted graph in step 1 The establishment process is as follows: any two nodes are connected by an edge, and the weight of the edge is the actual distance between the two nodes. Based on this, an approximate fully weighted graph of n nodes is established. , Where: is called the weight matrix, , Where: For city nodes and The straight-line distance between them; If any two nodes are connected by an edge, it means that any two cities are on land and communication lines can be directly laid. If any two nodes are not connected by an edge, it means that the two cities are across the ocean and communication lines cannot be directly laid.

[0006] Preferably, in step 1 The calculation process is as follows: Let the longitude and latitude coordinates of city i be ,in is the latitude coordinate, is the longitude coordinate. The minor arc length of the great circle passing through cities i and j on the earth is the actual distance between the two points. The center of the earth is the origin of the coordinates. , with the equatorial plane as plane, with the plane where the 0 degree meridian coil is located as The plane establishes a three-dimensional rectangular coordinate system. Assuming that the earth is a sphere, the rectangular coordinates of the two cities i and j are: , , in km is the radius of the earth, According to the arc length formula, the minor arc length of the great circle passing through cities i and j on the earth is ,in For vector The corresponding angle is, , , According to the vector inner product, we have , so the straight-line distance between cities i and j is: ,and , , So the unit vector: , , obviously , , , .

[0007] Preferably, in step 1: for the image , if there is a graph ,in , , so that the graph There is only one path connecting any two nodes in the graph. Connected and , represents the number of edges, represents the number of nodes, then T is called the spanning tree of G, is the weight of the spanning tree, Where: It is the edge The weight of the city , The actual distance between Smallest That is the minimum spanning tree of graph G; Use Kruskal algorithm to calculate the minimum spanning tree , specifically including the following steps: Step 1: Select , so that is the edge with the smallest weight; Step 2: If If selected, Select , so that There is no circle in the middle; yes The edge with the smallest weight; Step 3: Until you select until.

[0008] Preferably, the leaf node in step 2 specifically refers to a node whose destruction has little impact on the connectivity of the entire network. After the node is lost, the minimum spanning tree will be decomposed into several connected branches, and the number of nodes contained in each connected branch is different; The important node specifically refers to a node with good functions, which will directly determine the quality of the overall connectivity performance of the network. After the node is missing, the number of nodes in the connected branches is relatively large, and it is in a relatively "deep" layer in the network structure, and the number of controllable branch nodes below is large.

[0009] Preferably, the method for determining important nodes in step 2 is: when starting from different leaf nodes and searching upward layer by layer according to the network connection mode, the same node may have different layers in different branches. Therefore, the layers of each node in different branches and the number of nodes connected under the layer are recorded; the deeper the layers and the larger the number of nodes, the more important the position of the node in the network, specifically: The set of all nodes is , define three labels for each node, one to record the number of layers of the node in the network, represented by P, one to record the number of nodes connected to the next layer of the node, represented by Q, and one to record whether the node has been fully checked, represented by S. The set of all labeled and fully checked nodes is , the set of nodes that are labeled but not fully checked is ; The design labeling algorithm process is as follows: Initial situation: Each node in Layer number , Check the label ;node The degree is , , ; Step01: Find all degrees Nodes, i.e. leaf nodes, are labeled , , , , , , ; Step02: , ,like If there are edges connected, then give Label , ,in express Zhongyu The number of connected nodes, , , , , ; Step03: Judgment Is it true? If so, execute Step04; otherwise, execute Step02. Step04: Algorithm termination; It is stipulated that city nodes with no less than 9 node layers are important nodes. At the same time, the higher the degree of the node, the higher its importance.

[0010] Preferably, the communication network line optimization in step 3 specifically includes: adding multiple geographically independent communication branches near important nodes using the LDA edge adding strategy; Specifically: calculate the node degree of the network, select the two nodes with the lowest degree and add one edge, self-loops or duplicate edges are not allowed, and repeat the above algorithm until the specified line connection length is reached.

[0011] Preferably, the damaged network repair model established in step 4 is specifically: finding a new device node , and its set is called the candidate node set , construct a connection The connection method with the shortest total line length is solved The minimum spanning tree of , so that the minimum spanning tree Less than only Minimum spanning tree of nodes , thereby determining the node set The number and location of midpoints; Since there is only one road connecting any two cities, assume that the damaged device is a node , in the minimum spanning tree with The set of connected nodes is When the device is damaged, its nodes and its connected edges will be removed from the network, and the entire network will be decomposed into connected branches, where express The number of nodes in the .

[0012] Preferably, the step 4 specifically includes the following steps: Step A: When the number of nodes that need to be reconnected to repair the network does not exceed 4, the location of the device node is determined using the Steiner minimum tree construction principle; Step B: When the number of nodes that need to be reconnected to repair the network exceeds 4, decompose the nodes into combinations less than or equal to 4, and then use the method in Step A to determine the location of the device nodes, splice them, and solve them by enumeration traversal; Preferably, the Step A is as follows: The Steiner tree is constructed by adding virtual nodes, the set of these nodes is , calculated using Kruskal algorithm The minimum spanning tree of , so that its total length is as much smaller as possible than the length of the original node set The minimum spanning tree , The node in is called the origin. The points in are called Steiner points, and the Steiner tree containing k Steiner points is called a k-order Steiner tree; When the selection of supplementary nodes is different, the resulting Steiner tree is different. The purpose of the solution is to find the Steiner tree with the smallest weight sum, that is, the Steiner minimum tree; The Steiner tree has the following properties: Property 1: Let the origin of the Steiner minimum tree be Then the number of Steiner points ; Property 2: The angle between any two adjacent edges on the Steiner minimum tree is not less than 120°; Property 3: Any node on the Steiner minimum tree has no more than 3 associated edges, and each leaf point is the origin; (1) When When there are three origins A, B, and C, the Steiner minimum tree is to find a point P such that The sum of the distances is the smallest; according to property 1, only Steiner trees of order 0 and 1 can be constructed; Any interior angle in is greater than 120°. , now point P is point B, Minimum; The three interior angles are all less than 120°, and P is A point inside The sum is the smallest, only , point P is also called the Fermat point of the triangle; Suppose the edges of the origin minimum spanning tree are AB and BC, then the edges of the Steiner minimum tree are PA, PB, and PC. Suppose the longitude and latitude coordinates of point P are , the latitude and longitude coordinates of points A, B, and C are , , , then , The coordinates of points A, B, C, and P in the rectangular coordinate system are: , , , , , , , , , set up , , , , , , , , , , , , then , Solve After that, there , (2) When When , construct 0, 1, and 2 order Steiner trees, where the 0 order Steiner tree is the minimum spanning tree of the origin, and the distance from point P to A, B, and Q in the 2 order Steiner tree is the shortest, that is, , point Q is the same as point P.

[0013] The present application constructs a communication network with the shortest total laid lines based on the minimum spanning tree, and constructs a network repair model based on the Steiner minimum tree; based on the importance of each city node in the communication network construction, a network edge addition rule is constructed, and then a network repair model is constructed to improve the anti-destruction performance of the constructed network and reduce the cost. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 is a flow chart of the present invention; Figure 2 A schematic diagram of the straight-line distance between two cities. Figure 3 is a 1st-order Steiner tree with 3 origins; Figure 4 It is a Steiner tree with 4 nodes. DETAILED DESCRIPTION

[0015] The following is a specific implementation of the present invention with reference to the accompanying drawings to further illustrate the composition of the present invention.

[0016] Embodiment 1. A method for designing a survivable communication network, the specific process is as follows Figure 1 As shown, the following steps are included: 1. Establish a minimum spanning tree model to obtain the shortest communication network: select n communication cities as nodes of the wired communication network and establish an approximate fully weighted graph , in Figure Find the minimum spanning tree of n nodes , calculate the minimum spanning tree , obtain the communication network with the shortest total line connecting n communication cities; 2. Determine the important nodes of the network: In the communication network with the shortest total line constructed by the n nodes established in step 1, determine the leaf nodes and important nodes; 3. Optimize the communication network in step 1 for the important nodes obtained in step 2; 4. Establish a damaged network repair model.

[0017] Among them, the approximate fully weighted graph in step 1 The establishment process is as follows: any two nodes are connected by an edge, and the weight of the edge is the actual distance between the two nodes. Based on this, an approximate fully weighted graph of n nodes is established. , Where: is called the weight matrix, , Where: For city nodes and The straight-line distance between them; If any two nodes are connected by an edge, it means that any two cities are on land and communication lines can be directly laid. If any two nodes are not connected by an edge, it means that the two cities are across the ocean and communication lines cannot be directly laid.

[0018] Wherein, the step 1 The calculation process is as follows: Assume the longitude and latitude coordinates of city i are ,in is the latitude coordinate, is the longitude coordinate. The minor arc length of the great circle passing through cities i and j on the earth is the actual distance between the two points. The center of the earth is the origin of the coordinates. , with the equatorial plane as plane, with the plane where the 0 degree meridian coil is located as The plane establishes a three-dimensional rectangular coordinate system. Assuming that the earth is a sphere, the rectangular coordinates of the two cities i and j are: , , in km is the radius of the earth, According to the arc length formula, the minor arc length of the great circle passing through cities i and j on the earth is ,in For vector The corresponding angle is, , , According to the vector inner product, we have , so the straight-line distance between the two cities i and j is , and , , so the unit vector , , Apparently , , , .

[0019] Among them, in the step 1: for the figure , if there is a graph ,in , , so that the graph There is only one path connecting any two nodes in the graph. Connected and , represents the number of edges, represents the number of nodes, then T is called the spanning tree of G, is the weight of the spanning tree, Where: It is the edge The weight of the city , The actual distance between Smallest That is the minimum spanning tree of graph G; Use Kruskal algorithm to calculate the minimum spanning tree , specifically including the following steps: Step 1: Select , so that is the edge with the smallest weight; Step 2: If If selected, Select , so that There is no circle in the middle; yes The edge with the smallest weight; Step 3: Until you select until.

[0020] The leaf node in step 2 specifically refers to a node whose destruction has little impact on the connectivity of the entire network. After the node is lost, the minimum spanning tree will be decomposed into several connected branches, and the number of nodes contained in each connected branch is different; The important node specifically refers to a node with good functions, which will directly determine the quality of the overall connectivity performance of the network. After the node is missing, the number of nodes in the connected branches is relatively large, and it is in a relatively "deep" layer in the network structure, and the number of controllable branch nodes below is large.

[0021] The method for determining important nodes in step 2 is as follows: when starting from different leaf nodes and searching upward layer by layer according to the network connection mode, the same node may have different layers in different branches. Therefore, the layers of each node in different branches and the number of nodes connected to the layer are recorded; the deeper the layers and the larger the number of nodes, the more important the position of the node in the network, specifically: The set of all nodes is , define three labels for each node, one to record the number of layers of the node in the network, represented by P, one to record the number of nodes connected to the next layer of the node, represented by Q, and one to record whether the node has been fully checked, represented by S. The set of all labeled and fully checked nodes is , the set of nodes that are labeled but not fully checked is ; The design labeling algorithm process is as follows: Initial situation: Each node in Layer number , Check the label ;node The degree is , , ; Step01: Find all degrees Nodes, i.e. leaf nodes, are labeled , , , , , , ; Step02: , ,like If there are edges connected, then give Label , ,in express Zhongyu The number of connected nodes, , , , , ; Step03: Judgment Is it true? If so, execute Step04; otherwise, execute Step02. Step04: Algorithm termination; It is stipulated that city nodes with no less than 9 node layers are important nodes. At the same time, the higher the degree of the node, the higher its importance.

[0022] The communication network line optimization in step 3 is specifically as follows: using the LDA edge adding strategy to add multiple geographically independent communication branches near important nodes; Specifically: calculate the node degree of the network, select the two nodes with the lowest degree and add one edge, self-loops or duplicate edges are not allowed, and repeat the above algorithm until the specified line connection length is reached.

[0023] The damaged network repair model established in step 4 is specifically as follows: Find a new device node , and its set is called the candidate node set , construct a connection The connection method with the shortest total line length is solved The minimum spanning tree of , so that the minimum spanning tree Less than only Minimum spanning tree of nodes , thereby determining the node set The number and location of midpoints; Since there is only one road connecting any two cities, assume that the damaged device is a node , in the minimum spanning tree with The set of connected nodes is When the device is damaged, its nodes and its connected edges will be removed from the network, and the entire network will be decomposed into connected branches, where express The number of nodes in the .

[0024] Wherein, the step 4 specifically includes the following steps: Step A: When the number of nodes that need to be reconnected to repair the network does not exceed 4, the location of the combat readiness equipment node is determined using the Steiner minimum tree construction principle; Step B: When the number of nodes that need to be reconnected to repair the network exceeds 4, decompose the nodes into combinations less than or equal to 4, and then use the method of Step A to determine the location of the device nodes, splice them, and solve them by enumeration traversal.

[0025] The specific details of Step A are as follows: The Steiner tree is constructed by adding virtual nodes, the set of these nodes is , calculated using Kruskal algorithm The minimum spanning tree of , so that its total length is as much smaller as possible than the length of the original node set The minimum spanning tree , The node in is called the origin. The points in are called Steiner points, and the Steiner tree containing k Steiner points is called a k-order Steiner tree; When the selection of supplementary nodes is different, the resulting Steiner tree is different. The purpose of the solution is to find the Steiner tree with the smallest weight sum, that is, the Steiner minimum tree; The Steiner tree has the following properties: Property 1: Let the origin of the Steiner minimum tree be Then the number of Steiner points ; Property 2: The angle between any two adjacent edges on the Steiner minimum tree is not less than 120°; Property 3: Any node on the Steiner minimum tree has no more than 3 associated edges, and each leaf point is the origin; (1) When When there are three origins A, B, and C, the Steiner minimum tree is to find a point P such that The distance and the minimum; construct Steiner trees of order 0 and 1; Any interior angle in is greater than 120°. , now point P is point B, Minimum; The three interior angles are all less than 120°, and P is A point inside The sum is the smallest, only , point P is also called the Fermat point of the triangle; Assume that the edges of the origin minimum spanning tree are AB and BC, then the edges of the Steiner minimum tree are PA, PB, and PC, such as Figure 3 As shown, Assume the latitude and longitude coordinates of point P are , the latitude and longitude coordinates of points A, B, and C are , , , then , The coordinates of points A, B, C, and P in the rectangular coordinate system are , , , ,therefore , , , , , set up , , , , , , , , , , , , then , solve for After that, there , (2) When When , construct 0, 1, 2 order Steiner trees, such as Figure 4 As shown, the 0-order Steiner tree is the minimum spanning tree of the origin. The distance from point P to A, B, and Q in the 2-order Steiner tree is the shortest, that is, , point Q is the same as point P.

[0026] Example 2. This example is an analysis of the effect of Example 1, with specific reference to my country's communication network, as follows: In order to make the randomly selected 10% communication nodes more representative, MATLAB is used to perform stratified sampling on these n city nodes according to the proportion of the number of nodes of each degree to the total number of nodes. In this example, n is 139, and 14 communication nodes are selected each time, and these nodes are destroyed. At the same time, in order to better explore and illustrate the connectivity of the new communication network and eliminate the influence of accidental factors, the destruction of 10% of the communication nodes will be simulated three times, and three groups of new and old communication networks will be compared and analyzed, as shown in Table 1.

[0027] Table 1 Three groups of randomly selected communication nodes , When simulating the first group of communication node damage, the communication nodes of 14 cities including Duyun, Baicheng, Manchuria, Gejiu, Kunming, Tacheng, Pingxiang, Changchun, Nanjing, Huaihua, Xi'an, Yuncheng, Linfen and Longyan were damaged in the original minimum spanning tree network diagram and the new optimized communication network diagram, and the node damage was displayed on the map using MATLAB. Similarly, the second and third groups of communication node damage were simulated.

[0028] In order to evaluate the anti-attack performance of the network, the following evaluation indicators are given: 1. Maximum number of connected branch nodes: After a node in the communication network is damaged, the communication network will be decomposed into several connected branches. The number of nodes in the connected branch with the most nodes is the maximum number of connected branch nodes, which is recorded as .

[0029] The more nodes in the maximum connected branch, the more nodes in the network can remain connected when the network is damaged, so the damage of the network will have less impact on the connectivity performance.

[0030] 2. The network diameter of the largest connected branch: For a network with N nodes, two nodes and The distance between Defined as the number of edges in the shortest path connecting the two nodes, the maximum distance between any two nodes in the network is called the diameter of the network, denoted by ,Right now , The larger the network diameter of the largest connected branch is, the wider the coverage of the connected branch is, and the greater the effect of the communication network is.

[0031] 3. Number of connected branches: The more connected branches there are, the greater the degree of network segmentation after a node is damaged, the more difficult it is to repair the network, the lower the feasibility of synchronous information transmission, and the weaker the ability of the topological structure of the communication network to resist damage.

[0032] 4. The degree of deviation of each branch node from the average number of nodes: Combined with the definition of the number of branch nodes given in 1, the number of nodes contained in each branch can be calculated, and its average value and sample mean square error can be calculated. The mean square error is used to reflect the degree of deviation from the average number of nodes. The larger the mean square error, the more unbalanced the connected branches will be after the network is damaged. There will be some connected branches with fewer nodes. Such branches are more likely to lose control, thereby weakening the effective control range of the communication network.

[0033] Based on the above communication network performance indicators, the connection performance of each group of new and old communication networks is summarized and tabulated, see Table 2.

[0034] Table 2 Comparison of connectivity performance of new and old communication networks in each group , As can be seen from the table, the connectivity performance of the optimized communication network is higher than that of the original minimum spanning tree network, and the resistance is also stronger. When 10% of the communication nodes are damaged, the new communication network can still ensure that most of the network device nodes are in normal operation, and the network diameter of its largest connected branch is much larger than that of the original communication network, almost twice as large.

[0035] Considering the economics of building a network, define is the line growth rate.

[0036] , in, is the total length of the newly added network lines, is the total length of the original network line, The larger the network, the longer the additional line distance, and the greater the economic cost. After calculation, the new communication network designed .

[0037] Taking the connection performance of the above-mentioned networks into consideration, it is only necessary to spend 19.14% more economic expenditure on the basis of the original network to nearly double the connection performance of the network.

Claims

1. A method for designing a survivable communication network, characterized in that: The following steps are involved:

1. Establish a minimum spanning tree model to obtain the shortest communication network: select n communication cities as nodes of the wired communication network and establish an approximate fully weighted graph , in Figure Find the minimum spanning tree of n nodes , calculate the minimum spanning tree , obtain the communication network with the shortest total line connecting n communication cities; 2. Determine the important nodes of the network: In the communication network with the shortest total line constructed by the n nodes established in step 1, determine the leaf nodes and important nodes; 3. Optimize the communication network in step 1 for the important nodes obtained in step 2; 4. Establish a damaged network repair model.

2. The method for designing a survivable communication network according to claim 1, characterized in that: The approximate fully weighted graph in step 1 The establishment process is as follows: any two nodes are connected by an edge, and the weight of the edge is the actual distance between the two nodes. Based on this, an approximate fully weighted graph of n nodes is established. , Where: is called the weight matrix, , Where: For city nodes and The straight-line distance between the two surfaces.

3. A method for designing a survivable communication network according to claim 1 or 2, characterized in that: In step one The calculation process is as follows: Suppose the longitude and latitude coordinates of city i are ,in is the latitude coordinate, is the longitude coordinate. The minor arc length of the great circle passing through cities i and j on the earth is the actual distance between the two points. The center of the earth is the origin of the coordinates. , with the equatorial plane as plane, with the plane where the 0 degree meridian is located as The plane establishes a three-dimensional rectangular coordinate system. Assuming that the earth is a sphere, the rectangular coordinates of the two cities i and j are: , , in km is the radius of the earth, According to the arc length formula, the minor arc length of the great circle passing through cities i and j on the earth is ,in For vector The corresponding angle is, , , According to the vector inner product, we have , so the straight-line distance between cities i and j is: , and , , so the unit vector: , , Apparently , , , .

4. The method for designing a survivable communication network according to claim 3, characterized in that: In the step 1: for the figure , if there is a graph ,in , , so that the graph There is only one path connecting any two nodes in the graph. Connected and , represents the number of edges, represents the number of nodes, then T is called the spanning tree of G, is the weight of the spanning tree, Where: It is the edge The weight of the city , The actual distance between Smallest That is the minimum spanning tree of graph G; Use Kruskal algorithm to calculate the minimum spanning tree , specifically including the following steps: Step 1: Select , so that is the edge with the smallest weight; Step 2: If If selected, Select , so that There is no circle in the middle; yes The edge with the smallest weight; Step 3: Until you select until.

5. The method for designing a survivable communication network according to claim 3, characterized in that: The leaf node in step 2 specifically refers to a node whose destruction has little impact on the connectivity of the entire network. After the node is missing, the minimum spanning tree will be decomposed into several connected branches, and the number of nodes contained in each connected branch is different; The important node specifically refers to a node with good functions, which will directly determine the quality of the overall connectivity performance of the network. After the node is missing, the number of nodes in the connected branches is relatively large, and it is in a relatively "deep" layer in the network structure, and the number of controllable branch nodes below is large.

6. The method for designing a survivable communication network according to claim 5, characterized in that: The method for determining important nodes in step 2 is as follows: when starting from different leaf nodes and searching upward layer by layer according to the network connection mode, the same node may have different layers in different branches. Therefore, the layers of each node in different branches and the number of nodes connected to the layer are recorded; the deeper the layers and the larger the number of nodes, the more important the position of the node in the network, specifically: The set of all nodes is , define three labels for each node, one to record the number of layers of the node in the network, represented by P, one to record the number of nodes connected to the next layer of the node, represented by Q, and one to record whether the node has been fully checked, represented by S. The set of all labeled and fully checked nodes is , the set of nodes that are labeled but not fully checked is ; The design labeling algorithm process is as follows: Initial situation: Each node in Layer number , Check the label ;node The degree is , , ; Step01: Find all degrees Nodes, i.e. leaf nodes, are labeled , , , , , , ; Step02: , ,like If there are edges connected, then give Label , ,in express Zhongyu The number of connected nodes, , , , , ; Step03: Judgment Is it true? If it is true, execute Step04, otherwise execute Step02; Step04: Algorithm termination; It is stipulated that city nodes with no less than 9 node layers are important nodes. At the same time, the higher the degree of the node, the higher its importance.

7. The method for designing a survivable communication network according to claim 3, characterized in that: The communication network line optimization in step 3 is specifically: using the LDA edge addition strategy to add multiple geographically independent communication branches near important nodes; Specifically: calculate the node degree of the network, select the two nodes with the lowest degree and add one edge, self-loops or duplicate edges are not allowed, and repeat the above algorithm until the specified line connection length is reached.

8. The method for designing a survivable communication network according to claim 3, characterized in that: The damaged network repair model is established in step 4 as follows: Finding new device nodes , and its set is called the candidate node set , construct a connection The connection method with the shortest total line length is solved The minimum spanning tree of , so that the minimum spanning tree Less than only Minimum spanning tree of nodes , thereby determining the node set The number and location of midpoints.

9. The method for designing a survivable communication network according to claim 7, characterized in that: The step 4 specifically includes the following steps: Step A: When the number of nodes that need to be reconnected to repair the network does not exceed 4, the location of the combat readiness equipment node is determined using the Steiner minimum tree construction principle; Step B: When the number of nodes that need to be reconnected to repair the network exceeds 4, decompose the nodes into less than or equal to 4 combinations, and then use the method of Step A to determine the location of the device nodes, splice them, and solve them by enumeration traversal.

10. The method for designing a survivable communication network according to claim 9, characterized in that: The Step A is as follows: The Steiner tree is constructed by adding virtual nodes, the set of these nodes is , calculated using Kruskal algorithm The minimum spanning tree of , so that its total length is as much smaller as possible than the length of the original node set The minimum spanning tree , The node in is called the origin. The points in are called Steiner points, and the Steiner tree containing k Steiner points is called a k-order Steiner tree; When the selection of supplementary nodes is different, the resulting Steiner tree is different. The purpose of the solution is to find the Steiner tree with the smallest weight sum, that is, the Steiner minimum tree; (1) When When there are three origins A, B, and C, the Steiner minimum tree is to find a point P such that The sum of the distances is the smallest; according to property 1, only Steiner trees of order 0 and 1 can be constructed; Any interior angle in is greater than 120°. , at this time point P is point B, Minimum; The three interior angles are all less than 120°, and P is A point inside The sum is the smallest, only , point P is also called the Fermat point of the triangle; Suppose the edges of the origin minimum spanning tree are AB and BC, then the edges of the Steiner minimum tree are PA, PB, and PC. Suppose the longitude and latitude coordinates of point P are The longitude and latitude coordinates of points A, B, and C are , , , then , the coordinates of points A, B, C, and P in the rectangular coordinate system are: , , ， ， ， ， ， ， ， set up , , , , , , , , , , , , then , Solve After that, there , (2) When When , construct 0, 1, and 2 order Steiner trees, where the 0 order Steiner tree is the minimum spanning tree of the origin, and the distance from point P to A, B, and Q in the 2 order Steiner tree is the shortest, that is, , point Q is the same as point P.

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