Radio labeling system of strong product network model based on double-root tree and odd-order path

Abstract

The invention relates to the field of radio labeling, in particular to a radio labeling system of a strong product network model based on a double-root tree and an odd-order path. A strong product network model is obtained by calculating a strong product of the double-root tree model and the odd-order road model, and an assignment function for labeling radio stations is obtained by calculating the diameter, the assignment function and the lower bound of the strong product network model and establishing an ordered vertex sequence. The method comprises the following steps of: calculating a mark number value of each station as a frequency value, and establishing an ordered vertex sequence by sequentially selecting the vertex with the maximum vertex distance according to the vertex distance between the vertexes, so as to ensure that the vertex distance corresponding to any two adjacent vertexes in the ordered vertex sequence is maximum, thereby ensuring that when the electric-wire-free frequency is subsequently allocated, the working efficiency of the electric-wire-free frequency is greatly improved. The farther the station distance is, the closer the distributed radio frequency is; the problems that the frequency span obtained in the prior art is still large, and the demand of increasingly-scarce spectrum resources is difficult to meet are solved.

Description

Technical Field

[0001] The invention relates to the field of radio labeling, in particular to a radio labeling system based on a strong product network model of a double-rooted tree and an odd-order path. Background Art

[0002] Wireless communication technology is an indispensable part of daily life. The frequency allocation problem is a problem of reasonably allocating frequencies to network nodes in a wireless network. In order to prevent interference between frequency transmitters and receivers in the network, the frequency difference between nodes that are closer to each other in the network should be greater.

[0003] However, due to the shortage of spectrum resources, we need to minimize the frequency span. However, in current research, people propose to use vertex coloring of graphs to establish a graph theory model for the frequency allocation problem, requiring different frequencies to be allocated between adjacent nodes. More precisely, Hale first proposed to use graphs to model the frequency resource allocation problem, abstracting base stations into vertices. If there is an association between two vertices, that is, there is a connecting line between the two vertices, when there is an edge between the two base stations, interference will occur when communicating in the same frequency band. However, the frequency span obtained by existing technologies is still large, which is difficult to meet the demand for increasingly scarce spectrum resources. Summary of the invention

[0004] In view of the deficiencies of the prior art, the present invention provides a radio labeling system based on a strong product network model of a double-rooted tree and an odd-order path, which solves the problem that the frequency span obtained by the prior art is still large and it is difficult to meet the demand for increasingly scarce spectrum resources.

[0005] To achieve the above object, the present invention provides the following technical solutions:

[0006] A radio labeling system based on a strong product network model of a double-rooted tree and an odd-order path, the system comprising:

[0007] A strong product module, the strong product module is used to obtain the locations of several wireless communication base stations and the site data of whether there is data interaction between the base stations, and to construct a double-rooted tree model and an odd-order path model according to the site data, and to calculate the strong product of the two to obtain a strong product network model, and to obtain the central vertex and ordered vertex sequence of the strong product network model;

[0008] A radio label module, the radio label module is used to calculate the vertex distance, graph diameter and lower bound between any two vertices in the strong product network model, and calculate the radio label and corresponding span of the strong product network model;

[0009] A frequency allocation module is used for selecting a radio label with the smallest span as an optimal radio label and allocating frequencies to each vertex according to the optimal radio label.

[0010] Preferably, the strong product network module comprises:

[0011] A data acquisition module, the data acquisition module is used to obtain the locations of several wireless communication base station sites, and site data of whether each wireless communication base station site has data interaction;

[0012] A double-rooted tree model module, wherein the double-rooted tree model module is used to construct a double-rooted tree model according to the site data;

[0013] An odd-step road model module, wherein the odd-step road model module is used to construct an odd-step road model according to site data;

[0014] A strong product network model module, which is used to calculate the strong product of a double-rooted tree model and an odd-order path model to obtain a strong product network model, and obtain a central vertex and an ordered vertex sequence of the strong product network model.

[0015] Preferably, the step of obtaining the central vertex and the ordered vertex sequence by the strong product network model module is:

[0016] S1. Obtain the central vertex according to the strong product network model module; the expression of the central vertex is:

[0017]

[0018] In the above formula, C(V(G)) is the central vertex set of the strong product network model, y i is the i-th vertex in the central vertex set, X i Represents the i-th vertex y i The horizontal axis of , n represents the number of vertices in the odd-order path model;

[0019] S2. Calculate the vertex distance between each vertex in the strong product network model; the calculation formula for the vertex distance between any two vertices in the strong product network model is:

[0020] d((x n ,y n ), (x m ,y m ))=max{(d(x n , x m ), d(y n ,y m ))}

[0021] In the above formula, d((x n ,y n ), (x m ,y m )) represents two vertices (xn ,y n ) and (x m ,y m ), d(x n , x m ) and d(y n ,y m ) represent the two vertices x in the double-rooted tree model. n and x m The distance between the two vertices y in the odd-order path model n and m The distance between

[0022] S3. According to the vertex distances between the vertices, select the vertices with the largest vertex distances in turn to establish an ordered vertex sequence.

[0023] Preferably, the radio label module comprises:

[0024] A vertex distance acquisition module, wherein the vertex distance acquisition module is used to acquire the vertex distance between each vertex;

[0025] A graph diameter calculation module is used to calculate the diameter of a strong product network model. The calculation formula of the diameter of the strong product network model is:

[0026] diam(G)=diam(N)=n-1

[0027] In the above formula, diam(G) represents the diameter of the strong product network model, and diam(N) represents the diameter of the odd-order path model;

[0028] A lower bound calculation module, which is used to assign non-negative integer assignment functions to vertices in the strong product network model And for the ordered vertex sequence {u1, u2, u3, ..., u p},have and For all 1≤i≤p, the condition is satisfied, and then the lower bound of the radio label is calculated;

[0029] A span calculation module, which is used to obtain an assignment function The calculated label values ​​of each vertex are used to calculate the span between any two vertices based on the label values. The calculation formula for the span is:

[0030]

[0031] In the above formula, is the span, and Represents vertex ui and u j By assigning a function Calculate the results obtained.

[0032] Preferably, the frequency allocation module comprises:

[0033] An optimal assignment function acquisition module, the optimal assignment function acquisition module is used to calculate an optimal assignment function, the assignment function satisfies the condition when the equal sign in the expression of the lower bound calculation is established, and the span between any two vertices corresponding to the optimal assignment function is the smallest;

[0034] The vertex frequency allocation module is used to calculate the label value of each vertex according to the optimal assignment function, and use the label value as the frequency of each vertex.

[0035] Preferably, a comparison and analysis module is further included, wherein the comparison and analysis module is used to compare the vertex label ranges obtained by other models, and select the vertex label values ​​calculated by the model with the smallest label range as the actual frequency of each vertex.

[0036] Preferably, the double-rooted tree model module constructs a double-rooted tree model according to the following rules: select two sites w and w' as roots from the sites, assume that T is a double-rooted tree model with w and w' as roots, for any two vertices u and v, if u is on the path connecting w and v, then u is the ancestor of v, and v is the descendant of u, and the expression of the double-rooted tree model is M = (V1, E1), V1 = {x1, x2, x3, ..., x m}, where the two adjacent nodes are root nodes and the remaining nodes are leaf nodes.

[0037] As a preference, the rule for constructing an odd-order path model by the odd-order path model module is as follows: Assume that an odd-order path model N = (V2, E2) represents a path that is a finite non-empty sequence P n =y0e1y1e2…e k y n , whose entries are alternating vertices and edges such that for 1≤i≤k, edge e i The endpoint is y i-1 and i , then P is said to be from vertex y0 to vertex y n A path, vertex y0 and vertex y n are the starting point and end point of path P, respectively, and y1, y2, ... y n-1 is called its internal vertex. If the vertices along the path are different, then P is called a path. A path with n vertices is called P n , when the number of n is odd, it is called an odd-order path.

[0038] Preferably, the calculation rule for constructing the strong product network model by the strong product network model module is as follows: the strong product of the double-rooted tree model M and the odd-order path model N is Let G = (V, E), where V = V1 × V2, and the vertices (x n ,y n ) and (x m ,y m ) if and only if x n =x m ,y n y m ∈E2 or x n x m ∈E1,y n =y m or x n x m ∈E1,y n y m ∈E2, where x n ,x m ∈V1,y n ,y m ∈V2.

[0039] Preferably, the expression for calculating the lower bound of the radio label in the lower bound calculation module is as follows:

[0040]

[0041] In the above formula, d(u i ,u j ) represents the vertex u in the strong product network model i and u j The distance between and Represents vertex u i and u j By assigning a function The calculated result, diam(G), represents the diameter of the strong product network model.

[0042] Compared with the prior art, the present invention provides a radio labeling system based on a strong product network model of a double-rooted tree and an odd-order path, which has the following beneficial effects:

[0043] 1. The present invention constructs a double-rooted tree model and an odd-order path model according to the site data, thereby calculating the strong product of the two to obtain a strong product network model, and calculates the diameter, assignment function and lower bound of the strong product network model, and establishes an ordered vertex sequence to obtain an assignment function for labeling radio sites, so that the label value of each site can be calculated as a frequency value, thereby completing the labeling process of the radio sites.

[0044] 2. The present invention establishes an ordered vertex sequence by selecting vertices with the largest vertex distance in turn according to the vertex distance between each vertex, so as to ensure that the vertex distance corresponding to any two adjacent vertices in the ordered vertex sequence is the largest, thereby ensuring that when subsequently allocating radio frequency, the farther the site distance, the closer the allocated radio frequency, and the closer the site distance, the greater the difference in allocated radio frequency, thereby avoiding the frequencies of two radio sites that are close to each other interfering with each other due to being too close.

[0045] 3. The present invention constructs an assignment function that assigns a non-negative integer to each vertex, and calculates the label value of each vertex through the assignment function, and makes the label value increase in sequence with the order of the ordered vertex sequence, thereby ensuring that the label value of each site is different.

[0046] 4. The present invention compares the results calculated by the method mentioned in the present invention with other models to select the optimal frequency allocation result, thereby ensuring that in actual use, the frequency range used by the actual frequency allocation result is the smallest to minimize the occupied spectrum resources. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] The drawings described herein are used to provide a further understanding of the present application and constitute a part of the present application. The illustrative embodiments of the present application and their descriptions are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0048] Figure 1 It is a structural block diagram of the radio label system of the present invention;

[0049] Figure 2 It is a structural block diagram of the strong product module of the present invention;

[0050] Figure 3 It is a structural block diagram of the radio label module of the present invention.

[0051] In the figure: 1. Strong product module; 11. Data acquisition module; 12. Double-rooted tree model module; 13. Odd-order path model module; 14. Strong product network model module; 2. Radio label module; 21. Vertex distance acquisition module; 22. Graph diameter calculation module; 23. Lower bound calculation module; 24. Span calculation module; 3. Frequency allocation module; 31. Optimal assignment function acquisition module; 32. Frequency allocation module; 4. Comparative analysis module. DETAILED DESCRIPTION

[0052] In order to make the above-mentioned purposes, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific implementation methods, so that the implementation process of how the present application uses technical means to solve technical problems and achieve technical effects can be fully understood and implemented accordingly.

[0053] Those skilled in the art can understand that all or part of the steps in the following embodiments can be completed by instructing the relevant hardware through a program, so the present application can be in the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present application can be in the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program codes.

[0054] The frequency allocation problem is modeled by using a graph to simulate the topology of the network model. The graph is a binary group. For a given set of stations, a channel needs to be allocated to each station to avoid interference, and the span of the allocated channels is minimized. The channel is a positive integer. The interference level is related to the distance between the stations. For small distances, the interference is stronger, so geographically close stations must be allocated channels with large frequency differences, while for distant stations, the frequency difference can be small. This type of problem can be modeled by a graph, where the vertices represent stations, and each vertex is assigned a positive number, representing a channel, and each pair of adjacent stations is connected by an edge. A graph is denoted by G. For the graph G and any two vertices u and v in G, d(u, v) represents the distance between them. The maximum distance between any two vertices in G is called the diameter of G, denoted by diam(G). A vertex u with a vertex v (such as d(u, v) = diam(G)) is called a peripheral vertex. Since the topological structure of the strong product graph is a composite graph with high scalability, it allows the flexible construction of network structures of any scale through recursion or basic graph construction, which is particularly important when the network scale needs to be continuously expanded and in the process of expansion. It can keep its topological properties unchanged. Therefore, the radio labeling problem of the strong product graph has attracted the attention and exploration of more and more scholars, while the strong product graph of trees and paths has not been discussed so far.

[0055] Therefore, in order to solve the problem that the frequency span obtained by the existing technology is still large and it is difficult to meet the demand for increasingly scarce spectrum resources, this solution provides a radio labeling system based on a strong product network model of a double-rooted tree and an odd-order path, such as Figure 1-Figure 3 As shown, the optimal number of radio labels is given and the span is minimized. The system includes:

[0056] A strong product module 1 for obtaining the locations of several wireless communication base stations and the site data of whether there is data interaction between the base stations, and constructing a double-rooted tree model and an odd-order path model respectively according to the site data. The double-rooted tree model and the odd-order path model can use the graph theory toolbox of the MATLAB platform to simulate the topological structure of the network model, and calculate the strong product of the two to obtain the strong product network model, and obtain the central vertex and ordered vertex sequence of the strong product network model; a radio label module 2 for calculating the vertex distance, graph diameter and lower bound between any two vertices in the strong product network model, and calculating the radio label and the corresponding span of the strong product network model; a frequency allocation module 3 for selecting the radio label with the smallest span as the optimal radio label and allocating the frequency of each vertex according to the optimal radio label; thereby, the strong product network model constructed by the double-rooted tree model and the odd-order path model can meet the increasingly scarce spectrum resource demand by calculating the corresponding span and selecting the radio label value of each vertex with the smallest span as the radio frequency of each vertex.

[0057] In order to describe in detail the method for the strong product module 1 to obtain data and establish a double-rooted tree model, an odd-order path model and a strong product network model, the strong product module 1 includes:

[0058] A data acquisition module 11 for acquiring the locations of several wireless communication base station sites and site data of whether there is data interaction between each wireless communication base station site; a double-rooted tree model module 12 for constructing a double-rooted tree model according to the site data; the rule for the double-rooted tree model module 12 to construct the double-rooted tree model is as follows: two sites w and w' are selected from the site as roots, and T is a double-rooted tree model with w and w' as roots. For any two vertices u and v, if u is on the path connecting w and v, then u is the ancestor of v, and v is the descendant of u. The expression of the double-rooted tree model is M = (V1, E1), V1 = {x1, x2, x3, ..., x m}, where the two adjacent nodes are root nodes and the remaining nodes are leaf nodes;

[0059] The odd-order road model module 13 is used to construct an odd-order road model according to the site data; the rule for the odd-order road model module 13 to construct the odd-order road model is as follows: Assume that an odd-order road model N = (V2, E2) represents a path that is a finite non-empty sequence P n =y0e1y1e2…e k y n , whose entries are alternating vertices and edges such that for 1≤i≤k, edge e i The endpoint is y i-1 and i , then P is said to be from vertex y0 to vertex y n A path, vertex y0 and vertex yn are the starting point and end point of path P, respectively, and y1, y2, ... y n-1 is called its internal vertex. If the vertices along the path are different, then P is called a path. A path with n vertices is called P n ,When the number of n is odd, it is called an odd-order path;

[0060] A strong product network model module 14 is used to calculate the strong product of the double-rooted tree model and the odd-order path model to obtain a strong product network model, and obtain the central vertex of the strong product network model and an ordered vertex sequence; the calculation rule of the strong product network model module 14 to construct the strong product network model is as follows: the strong product of the double-rooted tree model M and the odd-order path model N is Let G = (V, E), where V = V1 × V2, and the vertices (x n ,y n ) and (x m ,y m ) if and only if x n =x m ,y n y m ∈E2 or x n x m ∈E1,y n =y m or x n x m ∈E1,y n y m ∈E2, where x n ,x m ∈V1,y n ,y m ∈V2;

[0061] The steps for the strong product network model module 14 to obtain the central vertex and the ordered vertex sequence are as follows:

[0062] S1. Obtain the central vertex according to the strong product network model module 14; the expression of the central vertex is:

[0063]

[0064] In the above formula, C(V(G)) is the central vertex set of the strong product network model 14, y i is the i-th vertex in the central vertex set, X i Represents the i-th vertex y i The horizontal axis of , n represents the number of vertices in the odd-order path model;

[0065] S2. Calculate the vertex distance between each vertex in the strong product network model; the calculation formula for the vertex distance between any two vertices in the strong product network model is:

[0066] d((x n ,y n ), (x m ,y m ))=max{(d(x n , x m ), d(y n ,y m ))}

[0067] In the above formula, d((x n ,y n ), (x m ,y m )) represents two vertices (x n ,y n ) and (x m ,y m ), d(x n , x m ) and d(y n ,y m ) represent the two vertices x in the double-rooted tree model. n and x m The distance between the two vertices y in the odd-order path model n and m The distance between

[0068] S3. According to the vertex distances between each vertex, select the vertices with the largest vertex distance in turn to establish an ordered vertex sequence; here, the central vertex can be selected as the first data of the ordered vertex sequence, and then the vertex with the largest vertex distance from the central vertex is selected as the second data of the ordered vertex sequence, and then the vertex with the largest vertex distance corresponding to the second data is selected as the third data of the ordered vertex sequence, and this cycle is repeated in sequence to obtain an ordered vertex sequence containing all sites, so as to ensure that the vertex distance corresponding to any two adjacent vertices in the ordered vertex sequence is the largest, so as to ensure that when allocating radio frequency in the future, the farther the site distance is, the closer the allocated radio frequency is, and the closer the site distance is, the greater the difference in the allocated radio frequency is, so as to avoid the frequencies of two radio sites that are close to each other interfering with each other due to being too close.

[0069] By studying the necessary and sufficient conditions for labeling radio sites using a strong product network model, the radio sites are labeled. According to the necessary and sufficient conditions, the radio labeling module 2 is planned. The module includes:

[0070] The vertex distance acquisition module 21 for acquiring the vertex distances between each vertex can be obtained by acquiring the vertex distances between each vertex calculated in the strong product network model module 14; the graph diameter calculation module 22 for calculating the diameter of the strong product network model, the calculation formula of the diameter of the strong product network model is:

[0071] diam(G)=diam(N)=n-1

[0072] In the above formula, diam(G) represents the diameter of the strong product network model, and diam(N) represents the diameter of the odd-order path model;

[0073] An assignment function used to assign non-negative integers to vertices in a strong product network model The lower bound calculation module 23, and for the ordered vertex sequence {u1, u2, u3, ..., u p},have and For all 1≤i≤p conditions, the lower bound of the radio label is then calculated; the expression for calculating the lower bound of the radio label in the lower bound calculation module 23 is as follows:

[0074]

[0075] In the above formula, d(u i ,u j ) represents the vertex u in the strong product network model i and u j The distance between and Represents vertex u i and u j By assigning a function The calculated result, diam(G), represents the diameter of the strong product network model;

[0076] Used to obtain the assignment function The span calculation module 24 calculates the span between any two vertices according to the calculated label values ​​of each vertex. The calculation formula of the span is:

[0077]

[0078] In the above formula, is the span, and Represents vertex u i and u j By assigning a function Calculate the results obtained.

[0079] Assignment Function There may be multiple expressions that all satisfy the lower bound calculation, but in order to save the occupation of radio spectrum resources, it is necessary to select the assignment function that minimizes the span. Therefore, the frequency allocation module 3 includes:

[0080] An optimal assignment function acquisition module 31 is used to calculate the optimal assignment function, which satisfies the condition when the equal sign in the expression of the lower bound calculation holds, and the span between any two vertices corresponding to the optimal assignment function is the smallest; a vertex frequency allocation module 32 is used to calculate the label value of each vertex according to the optimal assignment function, and use the label value as the frequency of each vertex.

[0081] In actual use, there are many model methods for frequency allocation to radio sites. In order to ensure that the frequency range used in the actual frequency allocation result is the smallest, it is necessary to compare the results calculated by the method mentioned in the present invention with other models to select the optimal frequency allocation result. Therefore, the system also includes a comparison analysis module 4, which is used to compare the vertex label range obtained by other models, and select the vertex label value calculated by the model with the smallest label range as the actual frequency of each vertex.

[0082] The above implementation methods have been described in detail. Specific examples are used herein to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as a limitation on the present invention.

Claims

1. A radio labeling system based on a strong product network model of a double-rooted tree and an odd-order path, characterized in that: The system includes: A strong product module (1), the strong product module (1) is used to obtain the locations of several wireless communication base stations and site data of whether there is data interaction between the base stations, and to construct a double-rooted tree model and an odd-order path model respectively according to the site data, and to calculate the strong product of the two to obtain a strong product network model, and to obtain a central vertex and an ordered vertex sequence of the strong product network model; A radio label module (2), the radio label module (2) is used to calculate the vertex distance, graph diameter and lower bound between any two vertices in the strong product network model, and calculate the radio label and corresponding span of the strong product network model; A frequency allocation module (3), wherein the frequency allocation module (32) is used to select the radio label with the smallest span as the optimal radio label and allocate frequencies to each vertex according to the optimal radio label.

2. The radio label system according to claim 1, characterized in that: The strong product module (1) comprises: A data acquisition module (11), the data acquisition module (11) is used to acquire the locations of a plurality of wireless communication base station sites, and site data of whether each wireless communication base station site has data interaction; A double-rooted tree model module (12), wherein the double-rooted tree model module (12) is used to construct a double-rooted tree model according to the site data; An odd-order road model module (13), wherein the odd-order road model module (13) is used to construct an odd-order road model according to site data; A strong product network model module (14) is used to calculate the strong product of a double-rooted tree model and an odd-order path model to obtain a strong product network model, and to obtain a central vertex and an ordered vertex sequence of the strong product network model.

3. The radio label system according to claim 1, characterized in that: The steps of obtaining the central vertex and the ordered vertex sequence by the strong product network model module (14) are as follows: S1. Obtain the central vertex according to the strong product network model module (14); the expression of the central vertex is: In the above formula, C(V(G)) is the central vertex set of the strong product network model (14), y i is the i-th vertex in the central vertex set, X i Represents the i-th vertex y i The horizontal axis of , n represents the number of vertices in the odd-order path model; S2, calculating the vertex distances between vertices in the strong product network model; The calculation formula for the vertex distance between any two vertices in the strong product network model is: d((x n ,y n ),(x m ,y m ))=max{(d(x n ,x m ),d(y n ,y m ))} In the above formula, d((x n ,y n ), (x m ,y m )) represents two vertices (x n ,y n ) and (x m ,y m ), d(x n , x m ) and d(y n ,y m ) represent the two vertices x in the double-rooted tree model. n and x m The distance between the two vertices y in the odd-order path model n and m The distance between S3. According to the vertex distances between the vertices, select the vertices with the largest vertex distances in turn to establish an ordered vertex sequence.

4. The radio label system according to claim 1, characterized in that: The radio label module (2) comprises: A vertex distance acquisition module (21), wherein the vertex distance acquisition module (21) is used to acquire the vertex distance between each vertex; A graph diameter calculation module (22), wherein the graph diameter calculation module (22) is used to calculate the diameter of the strong product network model. The calculation formula of the diameter of the strong product network model is: diam(G)=diam(N)=n-1 In the above formula, diam(G) represents the diameter of the strong product network model, and diam(N) represents the diameter of the odd-order path model; A lower bound calculation module (23), wherein the lower bound calculation module (23) is used to assign a non-negative integer value to the vertices in the strong product network model. And for the ordered vertex sequence {u1, u2, u3, ..., u p },have and For all 1≤i≤p, the condition is satisfied, and then the lower bound of the radio label is calculated; A span calculation module (24), wherein the span calculation module (24) is used to obtain an assignment function The calculated label values ​​of each vertex are used to calculate the span between any two vertices based on the label values. The calculation formula for the span is: In the above formula, is the span, and Represents vertex u i and u j By assigning a function Calculate the results obtained.

5. The radio label system according to claim 4, characterized in that: The frequency allocation module (3) comprises: An optimal assignment function acquisition module (31), the optimal assignment function acquisition module (31) is used to calculate an optimal assignment function, the assignment function satisfies the condition when the equal sign in the expression of the lower bound calculation is established, and the span between any two vertices corresponding to the optimal assignment function is the smallest; A vertex frequency allocation module (32) is used to calculate the label value of each vertex according to the optimal assignment function, and use the label value as the frequency of each vertex.

6. The radio label system according to claim 1, characterized in that: It also includes a comparison and analysis module (4), which is used to compare the vertex label ranges obtained by other models and select the vertex label values ​​calculated by the model with the smallest label range as the actual frequency of each vertex.

7. The radio label system according to claim 1, characterized in that: The double-rooted tree model module (12) constructs a double-rooted tree model according to the following rules: select two sites w and w' as roots from the sites, assume that T is a double-rooted tree model with w and w' as roots, for any two vertices u and v, if u is on the path connecting w and v, then u is the ancestor of v, and v is the descendant of u, and the expression of the double-rooted tree model is M = (V1, E1), V1 = {x1, x2, x3, ..., x m }, where the two adjacent nodes are root nodes and the remaining nodes are leaf nodes.

8. The radio label system according to claim 1, characterized in that: The rule for constructing the odd-order path model by the odd-order path model module (13) is as follows: Assume that a path represented by the odd-order path model N=(V2, E2) refers to a finite non-empty sequence P n =y0e1y1e2…e k y n , whose entries are alternating vertices and edges such that for 1≤i≤k, edge e i The endpoint is y i-1 and i , then P is said to be from vertex y0 to vertex y n A path, vertex y0 and vertex y n are the starting point and end point of path P, respectively, and y1, y2, ... y n-1 is called its internal vertex. If the vertices along the path are different, then P is called a path. A path with n vertices is called P n , when the number of n is odd, it is called an odd-order path.

9. The radio label system according to claim 1, characterized in that: The calculation rule of the strong product network model module (14) for constructing the strong product network model is as follows: The strong product of the double-rooted tree model M and the odd-order path model N is Let G = (V, E), where V = V1 × V2, and the vertices (x n ,y n ) and (x m ,y m ) if and only if x n =x m ,y n y m ∈E2 or x n x m ∈E1,y n =y m or x n x m ∈E1,y n y m ∈E2, where x n ,x m ∈V1,y n ,y m ∈V2.

10. The radio label system according to claim 4, characterized in that: The expression for calculating the lower bound of the radio signal in the lower bound calculation module (23) is as follows: In the above formula, d(u i ,u j ) represents the vertex u in the strong product network model i and u j The distance between and Represents vertex u i and u j By assigning a function The calculated result, diam(G), represents the diameter of the strong product network model.

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