CN116346202A - Wave beam hopping scheduling method based on maximum weighting group - Google Patents
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Abstract
The invention discloses a beam hopping scheduling method based on a maximum weight group, and belongs to the technical field of wireless communication networks. The method comprises the steps of firstly establishing a beam dispatching optimization model, then taking each wave position as a vertex to establish a weighted graph as a wave position set, obtaining weights by weighted summation of user/service distribution, time delay requirements and channel condition importance, and then searching a maximum weighted group in the graph through a maximum weighted group algorithm and dispatching the beam according to the weighted group. Simulation experiments show that the method weights the priorities of the user/service distribution, the link state and the QoS requirements, gives consideration to the influence of link loss, rain fade and the like between the user and the satellite, and different QoS requirements of different user service types on time delay, packet loss rate and the like, realizes the optimization of the capacity of the beam-hopping satellite communication system, flexibly schedules through the change of the weight, realizes the approximation of the system capacity under the dynamic environment, and better meets the QoS requirements of the user.
Description
Technical Field
The invention relates to a beam hopping scheduling method based on a maximum weight group, belonging to the technical field of wireless communication networks.
Background
In satellite communications, due to platform limitations, the power resources and bandwidth resources of the communications transponders are limited and cannot meet the increasing satellite communications service demands. The multi-beam technology mainly adopts a plurality of high-gain narrow beams to jointly cover a larger area, and can solve the problems of low power density, poor signal-to-noise ratio and the like existing in global/regional beam coverage. The multi-beam technology not only can improve the power utilization efficiency, but also can isolate users by beams, thereby achieving the effect of frequency multiplexing and further improving the frequency utilization efficiency, so that the multi-beam technology is adopted by more and more satellite communication systems. With the development of multi-beam antenna technology and the increasing number of beams, multi-beam communication is a necessary choice for future high throughput satellites (High Throughput Satellite, HTS).
The main characteristics of the conventional multi-beam satellite communication system can be summarized as follows:
(1) A large number of beams need to be managed, requiring many gateway stations to control;
(2) A single gateway station manages a given number of beams depending on the maximum bandwidth that can be handled;
(3) The adoption of a regular frequency multiplexing scheme and uniform power/bandwidth resource allocation cannot adapt to unbalanced service distribution scenes;
(4) When frequency multiplexing is performed, co-channel interference exists.
With the increasing types of satellite services, because each Beam usually has different service requirements and channel conditions due to different user positions and service requests, the spatial variability of the service requirements and the temporal variability of the service requirements are very obvious, and the traditional multi-Beam satellite system cannot meet the unbalanced characteristics of the satellite service requirements at this time, aiming at the background, researchers propose a new Beam-hopping (Beam-hopping) technical scheme, the basic idea is to use a time slicing technology, not all spot beams on a satellite work at the same moment, but only a part of beams work, and compared with the traditional multi-Beam satellite system, the new idea can meet the application scene of unbalanced service requirements, is a good technical choice of a future high-throughput satellite, and has the main advantages that:
(1) The method can support various services by using one carrier, the throughput of the repeater is obviously improved, only one complete carrier needs to be modulated/demodulated in each time slot slicing, and the working mode of a single carrier ensures that the amplifier does not need to give extra power back;
(2) The time slice period can be dynamically adjusted, so that the method can adapt to the changed service request and uneven service distribution, and can support various service terminals;
(3) The number of required power amplifiers and transmission channels is smaller;
(4) Through a space isolation mode, the interference among wave beams is obviously reduced, the frequency multiplexing can be better realized, and the frequency utilization rate is improved;
(5) Greatly reduces the cost of the gateway station.
Because of the above performance advantages, the beam hopping technique has attracted a great deal of attention, and researchers have made many beneficial studies from different angles in order to be able to better apply the beam hopping technique to practical satellite communication systems. The existing beam hopping scheme mainly considers user or service distribution, and obtains a beam hopping pattern through a beam hopping scheduling algorithm so as to match beam hopping and user/service distribution, and simultaneously avoids and reduces co-channel interference among beams. The main methods include deep learning, multi-objective optimization, dynamic clustering, linear/nonlinear programming, etc.
In a beam-hopping satellite communication system, the coverage area of a satellite is far larger than that of a ground mobile base station, and the number of users and the traffic of each wave position in the coverage area are also greatly different. Meanwhile, the same-frequency multiplexing is realized among beams of the beam hopping satellite communication system through space isolation, and the frequency utilization rate is improved. Therefore, in the traditional beam hopping satellite communication system, the scheduling of the beams is generally performed according to the user/service distribution and the same-frequency interference condition among the beams, and meanwhile, the fairness of time slot allocation among the beams is considered, the method matches the beam hopping and the user/service distribution through a certain optimization algorithm, and aims at maximizing the system capacity, so that the beams have more beam hops to the users/services, and have fewer beam hops to the users/services, and the utilization rate of the beams, the power and the frequency is improved. However, most of the existing methods only consider dynamic changes, fairness and suppression of co-channel interference among beams of user/service distribution, but consider very little for link state (propagation loss and rain fall) and delay requirements, so that the requirements of real-time service or delay-limited service are difficult to meet, and the changes of link capacities among different wave-level users and satellites are difficult to adapt, so that the scheduling of the beams does not reach an optimal state of capacity approximation, and the QoS requirements of users for speed, delay and the like are also difficult to meet.
Disclosure of Invention
Technical problem to be solved by the invention
The existing beam hopping scheduling method does not consider the difference and change of link states between a satellite and users in different wave positions, and also does not consider the requirements of different users or service types on time delay, packet loss rate and the like, so that the beam scheduling does not approach the link capacity, and the QoS requirements of the users are difficult to better meet. In order to solve the above problems, the present invention proposes a beam hopping scheduling method based on a maximum weight group.
Technical proposal
In order to achieve the above purpose, the technical scheme provided by the invention is as follows:
a method for beam hopping scheduling based on a maximum weight group comprises the following steps:
step 1, establishing a beam scheduling optimization model, wherein the method comprises the following steps:
let I be the time slot set of one hop-beam period, J be the beam set, K be the wave-bit set, I be the number of time slots in one hop-beam period, J be the number of wave-beams, K be the number of wave-bits, the scheduling problem of wave-beams and time slots is modeled as maximizing the system capacity:
satisfy the following requirements
Wherein: x is x i,j,k Indicating the beam on state, if beam j lights up bit k in slot i, x i,j,k =1, otherwise x i,j,k ＝0；
P (k) is the proportion of users/services in the kth wave position in the system;
R i,k representing the status of the slot i wave bit service requirement, if the wave bit k still needs service, R i,k =1, otherwise R i,k ＝0；
τ' represents the minimum number of slots allocated to a wave bit in 1 hop beam period;
step 2, regarding each wave bit as a vertex, establishing a weighted graph for the wave bit set K, wherein the weight of each wave bit/vertex is obtained by weighted summation of user/service distribution, time delay requirement and channel condition importance;
step 3, searching the maximum weighted group in the weighted graph obtained in the step 2;
and 4, scheduling the beam according to the weight group determined in the step 3.
Further, the step 2 includes the following steps:
step 21, defining the following set:
v: the wave bit/vertex set, i.e. the set of vertices in the weighted graph, contains all wave bits covered by satellites that need to be subjected to service and beam scheduling in the beam hopping period, expressed as v= { V k }(k∈K)；
W: the set of weights for the wave bits/vertices that each hop-beam period satellite beam needs to illuminate is denoted as w= { W k Weight of each wave bit/vertex in the set is obtained by weighted summation of user/service distribution, time delay requirement and channel condition importance;
Θ: any two wave beam direction included angle set, and it is assumed that the two wave beams respectively light wave bit k m And k n Then
Step 22, construct auxiliary graph G (V, E) for weighted vertex set, where V is the wave bit/vertex set, E is the edge set between vertices, when two wave bits k are lit up m And k n Are not adjacent and the included angle of the beam directions
At the time, wave position k m And k n Can be lightened by different beams at the same time, then the representative wave bit k m And k n Vertex of->
And->
The use of edge connection between>
θ c Represents the same-frequency interference avoidance threshold angle between two beams, when the included angle between the two beam directions is larger than theta c It is considered that there is no co-channel interference or interference between them is tolerable.
Further, the method for calculating the wave position/vertex weight in the step 2 is as follows:
wherein w is k Weights for vertices representing wave position k; alpha k,1 、α k,2 、α k,3 Weighting coefficients on the wave bit k for representing user/service distribution, time delay requirement and channel condition importance respectively; beta k,1 As the proportion of the user/traffic in the wave position k in the whole system, beta k,2 For the service priority, beta, of the user in the wave position k, related to time delay k,3 Is the sum of the user-dependent path loss and the rain fade in the bin k.
Further, step 3 comprises the steps of:
step 31, arranging all vertexes in the graph in descending order of weight to obtain a set v= { V 1 ,v 2 ,…,v K } satisfy w 1 ≥w 2 ≥…≥w K ；
Step 32, let the number of vertices K and V in the auxiliary graph G (V, E) k The vertex set with edge connection is N (v k ) Initializing a node { v } having the largest weight as the smallest weight K }，
Is provided with
k∈{1,2,…,K-1}；Q K ＝{v K }，
S k ＝{v k ,v k+1 ,…,v K }，k∈{1,2,…,K}，
Starting searching from the vertex with the smallest weight value in the auxiliary graph, and for vertex v k ：
When Q is k+1 ∪{v k When the number of the groups is 1, let Q k ＝Q k+1 ∪{v k And (3)
When Q is k+1 ∪{v k When the number of the groups is not 1, let Q k ＝{v k }，
S k ＝S k ∩N(v k ) And in sub-graph S of auxiliary graph k ＝{v k ,v k+1 ,…,v K Finding a new clique Q among } k ，
At the time of guaranteeing
On the premise of (1), update Q k ，/>
S k The above process is looped until vertex v 1 Until a maximum weight-cluster for the graph is found;
step 33, judging the potential of the maximum weighted cluster obtained in step 32, and if the potential is greater than the number J of beams, taking the first J elements of the maximum weighted cluster as the maximum weighted cluster.
Advantageous effects
The invention takes the dynamic change of the link and the QoS requirement of the user as important factors of scheduling when the beams are scheduled while considering the user/service distribution, fairness and the same frequency interference among the beams, and flexibly schedules by the change of the weight, thereby realizing the approximation of the system capacity under the dynamic environment and better meeting the QoS requirement of the user;
the method weights different priorities of user/service distribution, link state and QoS requirement, gives consideration to the influence of link loss, rain fade and the like between the user and the satellite and the different QoS requirements of different user service types on time delay, packet loss rate and the like, and the established beam scheduling mathematical model obtains a beam scheduling scheme with capacity approaching and comprehensively considering the optimization of the link state and QoS requirement, thereby realizing the optimization of the capacity of the beam hopping satellite communication system.
Drawings
FIG. 1 is a step diagram of a beam hopping scheduling method of the present invention;
FIG. 2 is a schematic diagram of a beam jump according to an embodiment of the method of the present invention;
FIG. 3 is a weighted graph of a set of wave positions constructed in accordance with an embodiment of the present invention;
FIG. 4 is a graph of throughput simulation experiment results of the method and the comparison method of the present invention;
FIG. 5 is a graph of experimental results of simulation of collision probability of the method of the present invention and the comparative method;
FIG. 6 is a graph of results of user satisfaction simulation for the method of the present invention and the comparative method.
Detailed Description
For a further understanding of the present invention, reference should be made to the following detailed description of the invention, taken in conjunction with the accompanying drawings and detailed description.
As shown in fig. 1, the method of the invention firstly builds a beam-jumping satellite beam dispatching optimization model, builds a weighted auxiliary graph for a wave-position set according to a new weighting method, puts forward a new maximum weighted-group algorithm on the basis of the weighted graph to carry out the optimized dispatching of the beam, and better adapts to the change of the link state and the QoS requirement of the user on the basis of realizing the change of the beam dispatching along with the user/service distribution.
Beam scheduling optimization model
In the existing beam scheduling period, the on-board processing module calculates and determines the beam and time slot allocation of the next beam scheduling period according to the user/service distribution of each wave bit and the beam interference parameter setting. In this scheduling process, the scheduling of beams and time slots is modeled to maximize system capacity:
wherein I is the number of time slots in 1 beam hopping period, J is the number of beams, and K is the number of wave bits; i is a time slot set of 1 wave-jumping beam period, J is a wave beam set, and K is a wave bit set; indicating the beam on state, if beam j lights up bit k in slot i, x i,j,k =1, otherwise x i,j,k =0; p represents the proportion of all wave position users/services in the whole system, P (k) is the proportion of the users/services in the kth wave position in the system; r is R i,k Representing the status of the wave bit service demand, if the wave bit k of the time slot i still needs service, R i,k =1, otherwise R i,k ＝0；k m 、k n Representing the wave position number; indicating the illumination of the wave bit k at time slot i m And k n The angle between the directions of the two beams,θ c represents the same-frequency interference avoidance threshold angle between two beams, when the included angle between the two beam directions is larger than theta c When no co-channel interference or interference between them is considered tolerable; τ' represents the minimum number of slots allocated to a wave bit in 1 hop beam period, which value ensures that each wave bit can be serviced within a certain time according to the system requirements. The fairness limit is given by the formula (2), so that more time slot resources are allocated to the wave bits with more users/services; equation (3) ensures that the number of allocated beams does not exceed the maximum number of beams available to the satellite; equation (4) shows that the light is turned on in time slot i, and the light wave bit k m And k n The included angle between the directions of the two beams is larger than the interference threshold theta c The method comprises the steps of carrying out a first treatment on the surface of the Equation (5) is a limit on the minimum number of slots to be allocated to each bin.
Node weighting
When weighting the nodes in the auxiliary graph, importance, time delay requirement and channel condition of the users/services are considered, the inter-beam interference limitation is selected and removed through connection between two points in the auxiliary graph, and fairness is determined through deleting the top point when the auxiliary graph is formed, namely the obtained service exceeds the proportion of the users/services, and the service is not involved in the construction of the auxiliary graph, namely the allocation of time slot resources and beam resources. In this embodiment, the weighting method is as follows,
wherein w is k Weights for vertices representing wave position k; alpha k,1 、α k,2 、α k,3 Weighting coefficients on the wave bit k for representing user/service distribution, time delay requirement and channel condition importance respectively; beta k,1 As the proportion of the user/traffic in the wave position k in the whole system, beta k,2 For the service priority, beta, of the user in the wave position k, related to time delay k,3 Is the sum of the user-dependent path loss and the rain fade in the bin k.
Building auxiliary graph
The following set is defined:
v: the wave bit/vertex set, i.e. the set of vertices in the weighted graph, contains all wave bits covered by satellites that need to be subjected to service and beam scheduling in the beam hopping period, expressed as v= { V k }(k∈K)；
W: the set of weights for the wave bits/vertices that each hop-beam period satellite beam needs to illuminate is denoted as w= { W k And (K epsilon K), and the weight calculation method of each wave bit/vertex in the weight set is as shown in the formula (6).
Θ: any two wave beam direction included angle set, and it is assumed that the two wave beams respectively light wave bit k m And k n Then
Building an auxiliary graph G (V, E) for a weighted set of vertices, where V is the set of wave bits/vertices defined above and E is the set of edges between vertices when two wave bits k are illuminated m And k n Are not adjacent and the included angle of the beam directions
At the time, wave position k m And k n Can be lightened by different beams simultaneously, and represents wave position k m And k n Vertex of->
And->
With edge connection->
θ c Represents the same-frequency interference avoidance threshold angle between two beams, when the included angle between the two beam directions is larger than theta c When it is considered that there is no co-channel interference or interference is tolerable
For any clique in the auxiliary graph
With any two vertices therebetweenWith edge connections, define the weight of the clique Q as the sum of the weights of all vertices in the clique, i.e.,
the maximum weighted cluster is the cluster with the sum of the maximum weights in the auxiliary graph, expressed as
Wherein Q is the set of all clique combinations in the auxiliary graph. Equation (8) is equivalent to the desired maximum number of users or maximum traffic or desired maximum system gain. In the invention, the maximum gain is used for measuring the effect of beam scheduling, and the gain is the sum of the weights of the scheduled wave bits/peaks, and reflects not only the throughput but also the service quality.
In this embodiment, a 9-wave-bit beam-hopping satellite communication system is provided, as shown in fig. 2. Assuming that two non-adjacent wave bits can be illuminated simultaneously, wave bit 1 can be illuminated simultaneously with wave bits 3,7, 9. However, bin 5 cannot be illuminated simultaneously with any other bin.
The auxiliary graph model is constructed according to fig. 2, and 9 wave bits are represented by 9 vertices, each of which is given a weight, as shown in fig. 3. After the auxiliary graph is constructed, the beam scheduling problem is converted into the problem of finding the largest weight cluster in the graph. In FIG. 3, several cliques can be found, e.g. { v 1 ,v 3 ,v 7 ,v 9 }、{v 1 ,v 6 ,v 7 }、{v 1 ,v 3 ,v 8 }、{v 2 ,v 7 ,v 9 }、{v 5 Etc., where the groups { v } 1 ,v 3 ,v 7 ,v 9 The largest weight is the largest weight in the auxiliary graph.
Maximum weight group algorithm
Assuming that the number of vertices in the auxiliary graph G (V, E) is K, vertex V k Is N (v) k ). Before starting the maximum weight-bolus algorithm, all vertices are first arranged in descending order of weight. As in the above graph, the rearranged vertices are v= { V 1 (v 7 ),v 2 (v 4 ),v 3 (v 3 ),v 4 (v 8 ),v 5 (v 5 ),v 6 (v 9 ),v 7 (v 2 ),v 8 (v 1 ),v 9 (v 6 ) The set of vertices after alignment is v= { V } 1 ,v 2 ,…,v K And w 1 ≥w 2 ≥…≥w K . The maximum weight group algorithm steps are as follows:
as can be seen from the maximum weight cluster scheduling algorithm above, when finding the vertex v k When there are two cases. When Q is k+1 ∪{v k When the number of the radicals is 1, Q k ＝Q k+1 ∪{v k And (3)
Otherwise, sub-graph S in auxiliary graph is needed k ＝{v k ,v k+1 ,…,v K Finding a new clique Q among } k . Based on the descending order of vertex weights, the addition of clique vertices begins with the minimum weight vertex j (v j ∈S k ) Wherein when->
At the time S k Updated to S k ＝S k ∩N(v k ). Addition of bolus vertices and S k Will continue to +.>
And find the containing roofPoint v k Is a maximum weight group of (c). Then the temporary maximum weight-group will be determined by comparing +.>
And
the clusters with higher weights will remain, and the process will continue until Q 1 。
In addition, the number of vertices of the maximum weight cluster cannot exceed the number of system beams, i.e. set Q m Is not greater than J. Therefore, at the end of the algorithm, the potential of the maximum weight cluster needs to be determined, and if it is greater than the number of beams, the first J elements of the maximum weight cluster are taken as the maximum weight cluster.
Jumping beam scheduling
The beams are scheduled according to a maximum weight-clique determined by a maximum weight-clique algorithm, which in the embodiment of fig. 2 is { v } 1 ,v 3 ,v 7 ,v 9 Then 4 beams illuminate bits 1,3, 7, 9 at the same time in the assigned time slot and perform the relevant traffic.
Experimental results
Fig. 4 and 5 show the system throughput (the number of packets successfully transmitted per hop beam period) and the collision probability simulation results during beam scheduling based on polling (Round robin), heuristic (Heuristic scheduling) and the maximum weight cluster algorithm (MWC scheduling) of the present invention in a hop-beam satellite communication system. Assuming a 25-bin user count of [500,300,0,3,1,3,11,13,15,27,16,24,21,25,8,13,7,8,2,1,1,0,1,0,0], where two-bin users occupy 80% of the total system user count, the maximum weight group assigns a greater weight to the user distribution to achieve the goal of maximizing system throughput. As can be seen from the figure, the system throughput is significantly improved by beam scheduling, and the MWC scheduling algorithm performance is better than the heuristic scheduling performance. And the collision probability of MWC scheduling is lower than heuristic scheduling. Further simulations indicate that in case of non-uniform user distribution, the throughput performance of using beam scheduling is close to that of uniform user distribution.
Fig. 6 shows the user satisfaction simulation results, with the simulation settings identical to the throughput and collision probability simulations. As can be seen from the figure, the user satisfaction of the beam polling schedule is very low in the wave positions with a large number of users, but can reach 100% in the wave positions with a small number of users. However, it is more desirable to be able to guarantee the demand of a large number of users and a large capacity demand of the wave positions. The heuristic and MWC beam scheduling can adjust the jump of the beam according to the user, service distribution and service requirements, so that the user satisfaction of the wave positions in the service set is obviously improved, and the user satisfaction of the MWC scheduling algorithm is superior to that of the heuristic algorithm, because the MWC algorithm can find the optimal wave position bright combination, and the throughput of the system is maximized; the complexity of the MWC algorithm is higher than that of the heuristic algorithm, requiring more computation time and on-board computing resources.
The invention and its embodiments have been described above by way of illustration and not limitation, and the invention is illustrated in the accompanying drawings and described in the drawings in which the actual structure is not limited thereto. Therefore, if one of ordinary skill in the art is informed by this disclosure, the structural mode and the embodiments similar to the technical scheme are not creatively designed without departing from the gist of the present invention.
Claims (4)
1. The method for beam hopping scheduling based on the maximum weight group is characterized by comprising the following steps:
step S1, a beam scheduling optimization model is established, and the method comprises the following steps:
let I be the time slot set of one hop-beam period, J be the beam set, K be the wave-bit set, I be the number of time slots in one hop-beam period, J be the number of wave-beams, K be the number of wave-bits, the scheduling problem of wave-beams and time slots is modeled as maximizing the system capacity:
satisfy the following requirements
Wherein: x is x i,j,k Indicating the beam on state, if beam j lights up bit k in slot i, x i,j,k =1, otherwise x i,j,k ＝0；
P (k) is the proportion of users/services in the kth wave position in the system;
R i,k representing the status of the slot i wave bit service requirement, if the wave bit k still needs service, R i,k =1, otherwise R i,k ＝0；
τ' represents the minimum number of slots allocated to a wave bit in 1 hop beam period;
s2, taking each wave bit as a vertex, and establishing a weighted graph for a wave bit set K, wherein the weight of each wave bit/vertex is obtained by weighted summation of user/service distribution, time delay requirement and channel condition importance;
step S3, searching the maximum weight group in the weight graph obtained in the step S2;
and step S4, scheduling the beam according to the weight group determined in the step S3.
2. The method for beam hopping scheduling based on the maximum weight group as claimed in claim 1, wherein said step S2 comprises the steps of:
step S21, defining the following set:
v: the wave bit/vertex set, i.e. the set of vertices in the weighted graph, contains all wave bits covered by satellites that need to be subjected to service and beam scheduling in the beam hopping period, expressed as v= { V k }(k∈K)；
W: the set of weights for the wave bits/vertices that each hop-beam period satellite beam needs to illuminate is denoted as w= { W k Weight of each wave bit/vertex in the set is obtained by weighted summation of user/service distribution, time delay requirement and channel condition importance;
Θ: any two wave beam direction included angle set, and it is assumed that the two wave beams respectively light wave bit k m And k n Then
Step S22, constructing an auxiliary graph G (V, E) for the weighted vertex set, wherein V is the wave bit/vertex set, E is the edge set between the vertices, when the two wave bits k are lighted up m And k n Are not adjacent and the included angle of the beam directions
At the time, wave position k m And k n Can be lightened by different beams at the same time, then the representative wave bit k m And k n Vertex of->
And->
The use of edge connection between>
θ c Represents the same-frequency interference avoidance threshold angle between two beams, when the included angle between the two beam directions is larger than theta c It is considered that there is no co-channel interference or interference between them is tolerable.
3. The method for beam hopping scheduling based on the maximum weight group as claimed in claim 2, wherein the method for calculating the wave position/vertex weight in step S21 is as follows:
wherein w is k Weights for vertices representing wave position k; alpha k,1 、α k,2 、α k,3 Weighting coefficients on the wave bit k for representing user/service distribution, time delay requirement and channel condition importance respectively; beta k,1 As the proportion of the user/traffic in the wave position k in the whole system, beta k,2 For the service priority, beta, of the user in the wave position k, related to time delay k,3 Is the sum of the user-dependent path loss and the rain fade in the bin k.
4. The method for beam hopping scheduling based on the maximum weight group as claimed in claim 1, wherein the step S3 comprises the steps of:
step S31, arranging all vertexes in the weighted graph in descending order of weight to obtain a set V= { V 1 ,v 2 ,…,v K } satisfy w 1 ≥w 2 ≥…≥w K ；
Step S32, let the number of vertices K and V in the auxiliary graph G (V, E) k The vertex set with edge connection is N (v k ) Initializing a node { v } having the largest weight as the smallest weight K }，
Is provided with
k∈{1,2,…,K-1}；Q K ＝{v K }，
S k ＝{v k ,v k+1 ,…,v K }，k∈{1,2,…,K}，
Starting searching from the vertex with the smallest weight value in the auxiliary graph, and for vertex v k ：
When Q is k+1 ∪{v k When the number of the groups is 1, let Q k ＝Q k+1 ∪{v k And (3)
When Q is k+1 ∪{v k When the number of the groups is not 1, let Q k ＝{v k }，
S k ＝S k ∩N(v k ) And in sub-graph S of auxiliary graph k ＝{v k ,v k+1 ,…,v K Finding a new clique Q among } k ，
At the time of guaranteeing
On the premise of (1), update Q k ，/>
S k The above process is looped until vertex v 1 Until a maximum weight-cluster for the graph is found;
and step S33, judging the potential of the maximum weighted group obtained in the step S32, and taking the first J elements of the maximum weighted group as the maximum weighted group if the potential is larger than the beam number J.
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