Graph Theory-Based Self-Organizing Network Throughput Maximization Time-Slot Scheduling Method

Abstract

A slot scheduling method for maximizing the throughput of an ad hoc network based on graph theory. A network model graph of the wireless ad hoc network is established and simplified so that the interference situation between nodes only exists between links that can communicate normally, enabling direct judgment through directed edges. The interference relationship between each pair of links is inferred, and the network model graph is transformed into a conflict graph. New constraints are added, and then new edges are added to the conflict graph to complete it into a complete graph. Along the links corresponding to the new edges, all slot scheduling schemes are obtained in a backtracking manner, with the search direction along the added edges in the complete graph and no old edges connected between any two points. The obtained slot scheduling schemes are traversed, and the prefix sum and suffix sum are used to quickly calculate the average value after removing the scheduling scheme of a certain interval, determine the selection or rejection of the current area scheduling scheme, and the number of obtained slot scheduling schemes is the final number of slots per frame. The present invention can improve the network throughput.

Description

Technical Field

[0001] The present invention belongs to the field of communication technologies, and particularly relates to a time slot scheduling method for maximizing the throughput of an ad hoc network based on graph theory, which can be used for time slot scheduling of a centralized ad hoc network. Background Art

[0002] The wireless ad hoc network is based on wireless communication technology and is a communication network technology that has been developed for more than fifty years. Compared with traditional communications, it has many characteristics such as being centerless, having fast network formation, and strong anti-destruction ability, expanding application scenarios that cannot be popularized by traditional networks, and providing a guarantee for realizing free communication anytime and anywhere. With the development of communication networks, concepts such as "Internet of Everything" have emerged one after another, and the implementation of many technologies and scenarios require the support of wireless ad hoc networks. Compared with traditional networks, the design of the medium access control layer protocol of wireless ad hoc networks is one of the important research objects. In a communication network based on time division multiple access, the time slot scheduling algorithm is a key issue that needs to be deeply studied.

[0003] The time slot scheduling algorithm can be divided into link-based scheduling and node-based scheduling based on different scheduling objects. These two different scheduling methods will have different degrees of influence on broadcast and unicast type services and network throughput. Link-based time slot scheduling can increase the sending opportunities of nodes and is more suitable for unicast services. Node-based time slot scheduling can make full use of the connectivity in the communication graph and is more suitable for broadcast services.

[0004] In existing time slot scheduling methods, by introducing relevant interference models and graph theory knowledge, the time slot scheduling algorithm is combined with graph theory, and the communication interference problem is transformed into a graph coloring problem. When using the graph coloring algorithm for time slot scheduling in existing methods, ensuring that a link is only scheduled once will result in a problem of waste of time slot resources.

[0005] Li Yize applied graph coloring technology to the resource scheduling of a multi-beam wireless ad hoc network system in his published paper "Resource Scheduling of a Multi-Beam Wireless Ad Hoc Network System Based on Coloring" (Computer Simulation, 2019, 36(02): 462-468), transformed the resource scheduling problem into an edge coloring problem, and abstracted the links with high load in the network into multiple virtual links, and assigned different colors to conflicting links. However, the deficiency is that: when performing time slot scheduling, the same link in the network occupies multiple time slots in a frame to achieve multiple calls of the link, and does not effectively improve the reuse rate of time slots.

[0006] That is, in existing graph coloring-based time slot scheduling algorithms, under the guarantee of absolute fairness of link scheduling, it is restricted that each link can only be colored once, that is, each link can only be scheduled once, and this way will undoubtedly lead to waste of time slot resources. Summary of the Invention

[0007] To overcome the shortcomings of the above-mentioned prior art, the purpose of the present invention is to provide a slot scheduling method for maximizing the throughput of an ad hoc network based on graph theory, so as to solve the problem of slot resource waste generated during slot scheduling based on the graph coloring algorithm in the prior art and improve the network throughput.

[0008] To achieve the above purpose, the technical solution adopted by the present invention is:

[0009] A slot scheduling method for maximizing the throughput of an ad hoc network based on graph theory includes the following steps:

[0010] S1: Establish a network model graph of the wireless ad hoc network and simplify it so that the interference situation between nodes only exists between links that can communicate normally, so that it can be directly judged through directed edges;

[0011] S2: Deduce the interference relationship between each link and transform the network model graph into a conflict graph;

[0012] S3: Add constraints, then add new edges in the conflict graph to complete it into a complete graph;

[0013] S4: Along the links corresponding to the new edges, obtain all slot scheduling schemes in a backtracking manner. The search direction is along the added edges in the complete graph, and there cannot be old edges connected between any two points;

[0014] S5: Traverse the slot scheduling schemes obtained in S4, use prefix sum and suffix sum to quickly calculate the average value after removing the scheduling schemes in a certain interval, and judge the selection or rejection of the current area scheduling scheme;

[0015] S6: The number of slot scheduling schemes obtained through S5 is the final number of slots per frame.

[0016] In one embodiment, in S1, the protocol interference model is adopted, and its interference radius R i is equal to the effective transmission radius R c , the network model graph is represented as a directed graph G, G=(V, E), V is the vertex set, V={v1, v2,..., v N}, v1, v2,..., v N are nodes, N is the number of nodes, E is the edge set, E={e1, e2,..., e L}, e1, e2,..., e L are links, L is the number of links. When the data sent by node v i can be normally received by node v j , it is considered that v i and v jA communication link can be formed between them, denoted as (i, j); the link (i, j) and the link (j, i) are two different links;

[0017] Define an N×N adjacency matrix C = {c ij}, which is used to represent the graph G to simplify the network model, where:

[0018]

[0019] In one embodiment, in the simplified network model graph of the S2, the interference relationship between each link is inferred according to the primary interference and the secondary interference, and the network model graph is converted into a conflict graph G c =(V c , E c );

[0020] In the conflict graph, the vertex set V c contains all the links, which are obtained by mapping the edge set E in the network model graph G, and each vertex corresponds to a directed edge; then according to the interference model, the interference link set of each link in the network model graph G is inferred. In the conflict graph G c the relationship between the links is reflected by the edge set E c ; if there is interference between the links, an undirected edge is used for connection;

[0021] According to the adjacency matrix C of the network model graph G and the protocol interference constraint conditions, the adjacency matrix of the conflict graph G c is constructed That is:

[0022]

[0023] In one embodiment, for the conflict graph G c , when a node cannot receive the data of two other nodes at the same time, or a node cannot send data to two targets at the same time, it is considered that the links marked 1 in each row or each column of the adjacency matrix C conflict with each other; when a node cannot receive and send data at the same time, or there is secondary interference, multiple loops are required for judgment.

[0024] In one embodiment, the S3, the new constraints include:

[0025] 3.1) Edge coloring is performed on the conflict graph G c , and the coloring times of each edge are multiple times, so that the link can communicate multiple times in one frame, that is:

[0026]

[0027] where represents the link e lWhether to schedule in the m-th time slot, i.e.:

[0028]

[0029] 3.2) The link scheduling scheme for each time slot must be different, i.e.:

[0030] 1 ≤ k, t ≤ M and k ≠ t

[0031] Wherein: represents the link scheme scheduled in the k-th time slot, represents the link scheme scheduled in the t-th time slot, and M represents the total number of time slots.

[0032] In one embodiment, in step S3, the new edges and the old edges are represented differently; in the adjacency matrix of the conflict graph G c the new edges are represented by 2, that is, by traversing the adjacency matrix GC of the complete graph and updating the values in the matrix, i.e.:

[0033]

[0034] In one embodiment, in step S5, the backtracking starts from the total number of links L and decreases from L to 1 in sequence. For each pending time slot allocation scheme, a hash table is used to record the vertices connected by all the old edges in the scheme and the number of repetitions, that is, the conflict set of the temporary scheduling scheme. By querying this table, it is quickly determined whether a new link can be added to this time slot scheme; when the number of links in the pending time slot scheduling scheme is equal to the specified number of links member_cnt, this time slot scheduling scheme is added to the time slot scheduling scheme set s[][], and at the same time, the maximum value array max_member[] for recording the link scheduling in the time slot scheduling scheme containing each link and the array node_num[] for recording the number of link scheduling times are updated. If the number of times each link is scheduled is greater than 0, the search ends.

[0035] In one embodiment, in step S6, starting from the end of the time slot scheduling scheme set s[][], the array section[][] is used to record the prefix sum of the link scheduling times in the time slot scheduling scheme and the change positions of the link scheduling times, and the array new_section[][] is used to record the suffix sum of the link scheduling times after deleting some time slot scheduling schemes and the remaining number of time slot scheduling schemes. Then, the average value after removing the time slot scheduling schemes in a certain area is quickly calculated, and the size of the number of links included in the current area scheduling scheme and the link average value of the total scheduling scheme is judged. If it is less than or equal to the average value, traverse this area and try to delete the scheduling schemes in this area while ensuring that the number of times each link is scheduled is greater than 0, and update new_section[][]; if it is greater than the average value, the algorithm ends.

[0036] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0037] Since the present invention provides a time slot allocation method in a wireless ad hoc network, that is, it improves and modifies the existing graph coloring-based algorithm, relaxes the limitation that each link can only be colored once, and relaxes the absolute fairness of link scheduling, and proposes a time slot allocation method based on graph theory, effectively solving the problem of waste of time slot resources in the prior art based on graph coloring, improving the reuse rate of time slot resources in the wireless ad hoc network, and further improving network throughput. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 is the implementation flowchart of the present invention.

[0039] Figure 2 is the interference model diagram of the present invention.

[0040] Figure 3 is the conflict graph of the network model in the present invention, where (a) is the network model and (b) is the conflict graph.

[0041] Figure 4 is the complete graph of the network model in the present invention, and the lines with small circles in the figure represent red lines. DETAILED DESCRIPTION OF THE INVENTION

[0042] The following will describe in detail the implementation manner of the present invention in conjunction with the drawings and embodiments.

[0043] As described above, for the link scheduling problem in resource allocation for a wireless ad hoc network using the TDMA method, the present invention rationally utilizes the design concept in graph coloring technology, constructs a conflict graph of the network model based on the network model, intuitively depicts the interference relationship between links, and simplifies the problem of avoiding conflicts in time slot scheduling. Specifically, by relaxing the limitation that each link can only be scheduled once and relaxing the absolute fairness of link scheduling, the mathematical model is reconstructed to improve the reuse rate of time slots and further improve network throughput. In terms of implementation means, the time slot scheduling is transformed into a graph coloring problem, and by constructing a complete graph of the network model, the graph coloring problem is transformed into an optimal combination search problem to facilitate the use of existing algorithms for solution optimization.

[0044] The specific process of the time slot scheduling method for maximizing the throughput of the self-organizing network based on graph theory of the present invention can refer to Figure 1 , and includes the following steps:

[0045] Step 1: Simplify the network model.

[0046] In the existing network model, the commonly used interference models are mainly the physical interference model and the protocol interference model. In the interference model, it is assumed that the effective transmission radius is Rc , the interference radius is R i , usually R i > R c .

[0047] The interference model used in this embodiment is the protocol interference model. In the protocol interference model, it is mainly divided into primary interference and secondary interference. The primary interference is as shown in (a), (b), and (c) in Figure 2 , where (a) means that a node cannot receive data from two other nodes simultaneously, (b) means that a node cannot send data to two destinations simultaneously, and (c) means that a node cannot receive and send data simultaneously. The secondary interference is as shown in (d), (e), and (f) in Figure 2 , which means that when a node is transmitting data normally, it will interfere with nodes whose Euclidean distance is less than R i , causing the node to be unable to correctly receive data.

[0048] In this embodiment, it is assumed that Ri = Rc. At this time, the situation of mutual interference but not meeting the communication conditions will not occur. The actual network can be abstracted as a directed graph G=(V, E) for description, where G is a directed graph. Suppose there are N nodes and L links in the network, where the vertex set V = {v1, v2,..., v N}, representing the set of nodes in the network, and the edge set E = {e1, e2,..., e L}, representing the set of transmission links between vertices. v1, v2,..., v N are nodes, N is the number of nodes, e1, e2,..., e L are links, and L is the number of links. When the data sent by node v i can be normally received by node v j , it is considered that a communication link can be formed between v i and v j , denoted as (i, j). The links (i, j) and (j, i) are denoted as two different links. The link (i, j) can generate a number corresponding to the edge in the edge set E through the function h(i, j), that is:

[0049] (i, j) = e h(i,j)

[0050] Define an N×N adjacency matrix C = {c ij} to represent the graph G and simplify the network model, where:

[0051]

[0052] Through this step, the interference situation between nodes only exists between links that can communicate normally, and can be directly judged through directed edges, simplifying the network model.

[0053] Step 2: Construct a conflict graph.

[0054] In the simplified network model, it is considered that the Euclidean distance between connected nodes in graph G satisfies the communication condition. At this time, the abstracted network model graph G=(V, E) can intuitively display the relationship between communication nodes and links, but the interference relationship between links is not obvious. Based on the simplified network model graph, the interference relationship between each link is inferred according to the primary interference and secondary interference, and the network model graph is converted into a conflict graph G c =(V c ,E c ).

[0055] 2.1) In the conflict graph, the vertex set V c contains all links, which can be obtained by mapping the edge set E in the network model graph G. At this time, each vertex corresponds to a directed edge. Then, according to the interference model, the interference link set of each link in graph G is inferred. In the interference graph G c , the relationship between links is reflected by the edge set E c . If there is interference between links, an undirected edge is used for connection. To distinguish between primary interference and secondary interference, primary interference is connected with a solid line, and secondary interference is connected with a dotted line. If the communication device uses a directional antenna for data transmission, the dotted line part can be ignored in the conflict graph.

[0056] As Figure 3 shown, Figure 3 in (a) is a network model graph containing directed edges, and (b) is the conflict graph corresponding to this communication network. It can be seen from the figure that there is a corresponding relationship between the conflict graph nodes and the directed edges in the network model graph, which can clearly show the conflict relationship between each link in the network.

[0057] 2.2) According to the adjacency matrix C of the known network model graph G and the protocol interference constraint conditions, construct the adjacency matrix c of the conflict graph G That is:

[0058]

[0059] That is, if e h(i,j) and e h(k,l) are two different edges in graph G and interfere with each other, then gc[h(i, j)][h(k, l)] = 1, otherwise gc[h(i, j)][h(k, l)] = 0. It can be found from the adjacency matrix of graph G that due to the conflict caused by half-duplex, it can be considered that the link with the flag of 1 in the matrix conflicts with the reverse link. For the first two cases of primary interference, it can be considered that the links with the flag of 1 in each row or each column of matrix C conflict with each other; for the third case of primary interference and secondary interference, multiple loops are required for judgment.

[0060] Step 3: Add constraints.

[0061] The edge coloring algorithm and vertex coloring algorithm of graphs are typical NP-complete problems. A simple way for edge coloring is to use a greedy strategy. The final result of coloring is that each edge is colored only once, and the minimum number of colors is obtained. Corresponding to time slot scheduling, it means obtaining the minimum period for each link to be scheduled once. Since the coloring order starts from the one with the largest number of conflicts, in the obtained result, the number of edges of a single color may not be the maximum, that is, the maximum multiplexing rate of a single time slot cannot reach the maximum. At the same time, because only one scheduling can be performed, for some links with fewer conflicts, they should have been able to be transmitted in multiple time slots, but now only one time slot is allowed for transmission, resulting in a problem of waste of time slot resources.

[0062] 3.1) To address the above problems and improve the multiplexing rate of time slot resources, the restriction that each edge can only be colored once can be relaxed. When performing edge coloring on the conflict graph G c each edge can be colored multiple times, so that the link can communicate multiple times in one frame, that is:

[0063]

[0064] where represents whether the link e l is scheduled in the m-th time slot, that is:

[0065]

[0066] At the same time, if multiple scheduling is performed while ensuring absolute fairness of the link, the time slot multiplexing rate will not increase. Therefore, only multiple scheduling of the link is considered, without guaranteeing absolute fairness of the scheduling.

[0067] 3.2) Due to the limitation of the network topology, when a certain link must be scheduled, the number of links that can be transmitted in that time slot cannot reach the maximum. Define the number of links that can be scheduled in a single time slot as ρ m , assume the maximum value of the number of links that can be scheduled in a single time slot is ρ mmax , and the minimum value is ρ mmin . To avoid continuously repeating the same time slot allocation method and introducing more ρ mmax to average ρ mmin , resulting in the combination number tending to infinity and ρ tending to ρ mmax . Therefore, an additional constraint needs to be added that the link scheduling scheme for each time slot must be different, that is:

[0068] 1 ≤ k, t ≤ M and k ≠ t

[0069] where: Denote the link scheme scheduled in the k-th time slot. Denote the link scheme scheduled in the t-th time slot, and M represents the total number of time slots.

[0070] Step Four: Complete the conflict graph into a complete graph.

[0071] According to the constraints described above, the goal of the solution can be reflected as finding multiple vertex combination methods in the conflict graph. If directly searching for combination methods in the conflict graph is relatively difficult, so new edges can be added to the conflict graph to complete it into a complete graph. As Figure 4 shown, complete the conflict graph shown in Figure 4 into a complete graph. For easy distinction, new edges and old edges are represented differently. In this embodiment, the newly added edges are represented in red. In this embodiment, it is assumed that Ri = Rc, so in the complete graph, the primary interference and the secondary interference are uniformly represented by solid lines.

[0072] In the adjacency matrix of the conflict graph G c , the newly added edges are represented by 2 to distinguish that these are the later added edges. That is, by traversing the adjacency matrix GC of the complete graph, update the values in the matrix:

[0073]

[0074] Step Five: Solve all combination methods according to the complete graph.

[0075] In the complete graph, the algorithm can search for multiple combinations along the red-marked edges. During the search process, it is determined whether a member joins the combination by judging whether there is a black edge connecting between members. That is, all combination methods (i.e., all time slot scheduling schemes) are obtained in a backtracking manner along the later-added links of the conflict graph Gc, and the search direction is along the route where gc[i][j] is 2 (i.e., the added edges in the complete graph), and at the same time, it is required that there cannot be old edges connecting between any two nodes.

[0076] The backtracking algorithm starts from the maximum number of members in the combination, i.e., L, but usually doesn't succeed the first time. The number of members decreases from L to 1. For each pending combination number (i.e., time slot allocation scheme), a hash table is used to record the vertices connected by all the old edges (i.e., black edges in this embodiment) in the members and the repetition times, which is the conflict set of the temporary combination. Therefore, whether a new member can be added to the combination can be quickly determined by querying this table. When the number of links in the pending combination is equal to the specified number of links member_cnt, this combination is added to the result set (i.e., time slot scheduling scheme set) s[][], and at the same time, the maximum member array max_member[] and the node array node_num[] are updated. If all values in the node array node_num[][] are greater than 0, that is, the scheduling times of each link are greater than 0, the search ends. Among them, the maximum member array max_member[] is used to record the maximum value array of link scheduling in the time slot scheduling scheme containing each link; the node array node_num[] is used to record the array of link scheduling times.

[0077] According to Figure 4 For the complete graph shown, in this embodiment, eight combinations can be obtained: {e12, e43}, {e12, e45}, {e21, e34}, {e21, e54}, {e23, e54}, {e32, e45}, {e34, e25}, {e43, e52}. At this time, the maximum number of members of each node is 2, and the number of colors used by all nodes is greater than 0. Therefore, the algorithm search ends.

[0078] Step 6: Solve the optimal combination.

[0079] Traverse from the end of the result set, i.e., the time slot scheduling scheme set s[][]. Use the array section[][] to record the prefix sum of the link scheduling times and the change positions of the link scheduling times in the time slot scheduling scheme, and use the array new_section[][] to record the suffix sum of the link scheduling times after deleting some time slot scheduling schemes and the remaining number of time slot scheduling schemes; then quickly calculate the average value after removing the time slot scheduling schemes in a certain area, and judge the size of the number of members (i.e., scheduling scheme) in the current area and the link average value of the total scheduling scheme. If it is less than or equal to the average value, traverse this area, and on the premise that the scheduling times of each link are greater than 0, try to delete the scheduling schemes in this area and update new_section[][]; if it is greater than the average value, the algorithm ends.

[0080] In this embodiment, traversing from back to front, it is found that the average number of members is equal to the number of members, both are 2. Then delete {e12, e45}, {e21, e34} or {e12, e43}, {e21, e54}.

[0081] In the present invention, the members of each scheme are the links scheduled in each time slot.

[0082] Step 7: Calculate the number of time slots and the time slot reuse rate.

[0083] The number of time slot scheduling schemes obtained in the previous step is the number of time slots in each frame finally. Assume that after the time slot allocation is completed, each frame is divided into M time slots. Define a two-dimensional matrix S = {s ml}.

[0084] When analyzing the reuse rate of time slot resources, the number of links scheduled in each time slot, that is, the reuse rate of a single time slot, can be calculated. Define the reuse rate of the m-th time slot as:

[0085]

[0086] Then the reuse rate of the time slot resources of the whole network is:

[0087]

[0088] The number of time slots required finally can be obtained through the array s[][], and the sum of node_num[] is the total number of communication links.

[0089] In this embodiment, the algorithm finally outputs M as 6, the total number of nodes as 12, and the time slot reuse rate ρ as 2.

[0090] The above description is only a specific example of the present invention and does not constitute any limitation to the present invention. Obviously, for professionals in the field, after understanding the content and principle of the present invention, various modifications and changes in form and details may be made without departing from the principle and structure of the present invention. However, these corrections and changes based on the idea of the present invention are still within the protection scope of the claims of the present invention.

Claims

1. A slot scheduling method for maximizing the throughput of an ad hoc network based on graph theory, characterized in that, It includes the following steps: S1: Establish a network model diagram of the wireless ad-hoc network and simplify it so that the interference situation between nodes only exists between links that can communicate normally, so that it can be directly judged through directed edges; S2: Deduce the interference relationship between each link and transform the network model diagram into a conflict graph; S3: Add new constraints, and then add new edges in the conflict graph to complete it into a complete graph; S4: Along the links corresponding to the new edges, obtain all time slot scheduling schemes in a backtracking manner. The search direction is along the added edges in the complete graph, and there cannot be old edges connected between any two points; S5: Traverse the time slot scheduling schemes obtained in S4, and use prefix sum and suffix sum to quickly calculate the average value after removing the scheduling scheme of a certain interval, and judge the selection of the current area scheduling scheme; S6: The number of time slot scheduling schemes obtained through S5 is the final number of time slots per frame; Wherein: The above-mentioned S1 adopts a protocol interference model and sets its interference radius R i equal to the effective transmission radius R c , and the network model diagram is represented as a directed graph G, G = (V, E), where V is the vertex set, V = {v1, v2, …, v N}, v1, v2, …, v N are nodes, N is the number of nodes, E is the edge set, E = {e1, e2, …, e L}, e1, e2, …, e L are links, L is the number of links. When the data sent by node v i can be normally received by node v j , it is considered that a communication link can be formed between v i and v j , denoted as (i, j); Define an N×N adjacency matrix C = {c ij}, which is used to represent graph G and realize the simplification of the network model, where: In the simplified network model diagram, according to the primary interference and secondary interference, infer the interference relationship between each link, and convert the network model diagram into a conflict graph G c =(V c , E c ); In the conflict graph, the vertex set V c contains all the links, which are obtained by mapping through the edge set E in the network model graph G, and each vertex corresponds to a directed edge; then, according to the interference model, the interference link sets of each link in the network model graph G are inferred. In the conflict graph G c the relationships between the links are reflected by the edge set E c If there is interference between the links, they are connected using undirected edges; Construct a conflict graph \(G\) based on the adjacency matrix \(C\) of the network model graph \(G\) and the protocol interference constraint conditions c of the adjacency matrix That is: The conflict graph G c In it, when a node cannot receive data from two other nodes simultaneously, or a node cannot send data to two destinations simultaneously, it is considered that the links marked as 1 in each row or each column of the adjacency matrix C conflict with each other; when a node cannot receive and send data simultaneously, or there is secondary interference, multiple loops are required for judgment; In step S3, the new constraints include: 3.1) Edge-color the conflict graph G c with each edge being colored multiple times, so that the link can communicate multiple times within one frame, that is: Among them indicates link e l whether it is scheduled in the m-th time slot, that is: 3.2) The link scheduling schemes for each time slot must be different, that is: 1 ≤ k, t ≤ M and k ≠ t Wherein: represents the link scheme scheduled in the k-th time slot, represents the link scheme scheduled in the t-th time slot, and M represents the total number of time slots; In the step S3, the new edge and the old edge are represented differently; in the adjacency matrix of the conflict graph G c , the new edge is represented by 2. That is, by traversing the adjacency matrix GC of the complete graph, the values in the matrix are updated, i.e.: In step S5, the backtracking starts from the total number of links L and decreases from L to 1 in turn. For each pending time slot allocation scheme, use a hash table to record the vertices connected by all old edges in the scheme and the repetition times, that is, the conflict set of the temporary scheduling scheme, and quickly judge whether a new link can be added to this time slot scheme by querying this table; when the number of links in the pending time slot scheduling scheme is equal to the specified number of links member_cnt, add this time slot scheduling scheme to the time slot scheduling scheme set s[][], and at the same time update the array max_member[] for recording the maximum value of link scheduling in the time slot scheduling scheme containing each link and the array node_num[] for recording the link scheduling times. If the scheduling times of each link are greater than 0, the search ends; In step S6, start traversing from the end of the time slot scheduling scheme set s[][]. Use the array section[][] to record the prefix sum of the link scheduling times in the time slot scheduling scheme and the change position of the link scheduling times, and use the array new_section[][] to record the suffix sum of the link scheduling times after deleting some time slot scheduling schemes and the remaining number of time slot scheduling schemes, and then quickly calculate the average value after removing the time slot scheduling scheme of a certain area, and judge the size of the number of links included in the current area scheduling scheme and the link average value of the total scheduling scheme. If it is less than or equal to the average value, traverse this area and try to delete the scheduling scheme of this area on the premise that the scheduling times of each link are greater than 0, and update new_section[][]; if it is greater than the average value, the algorithm ends; After the time slot allocation is completed, each frame is divided into M time slots, and a two-dimensional matrix S of M×L is defined as S = {s ml}; When analyzing the reuse rate of time slot resources, calculate the number of links scheduled for each time slot, that is, the reuse rate of a single time slot. Define the reuse rate of the mth time slot as: Then the reuse rate of the whole network time slot resources is: Obtain the final required number of time slots through the array s[][], and sum the node_num[] to get the total number of communication links.

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