Virtual network mapping method based on request pre-partition in sky-ground integrated network

Abstract

The application belongs to the field of virtual network mapping of space-ground integration, discloses a virtual network mapping method based on request pre-segmentation in a space-ground integrated network, designs a hierarchical mapping architecture based on a space-time resource tree, and completes the mapping process of the request based on the same; when the request arrives, if the resource amount of the sub-domain where the request access point is located cannot meet the required resource of the request, an improved body mapping label propagation algorithm is used to extract the high-order characteristics of the request, the low-order characteristics are combined for label propagation, so that the request is pre-segmented, and a suitable sub-domain for the pre-segmentation result is found for mapping. The application realizes the space controllability of the request mapping result, and can also reduce the remapping of the mapping result along the time dimension as much as possible, improve the resource utilization rate and the mapping success rate.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of virtual network mapping in the integration of space and ground, and particularly relates to a virtual network mapping method based on request pre-segmentation in the integration of space and ground network. BACKGROUND

[0002] The integration of space and ground network is a multi-domain fusion network, which is based on the ground network and supplemented by satellite network to form a wide coverage and easily expandable network structure, thereby enhancing the network function, realizing ubiquitous connection and better meeting the growing network demand, and solving the problems of limited coverage and service function of the traditional ground network. The resources in the integration of space and ground network have multidimensionality, and through deep fusion of different network systems, the ubiquitous communication demand in the network can be met, such as disaster relief, spaceflight and navigation, and better service can be provided for users.

[0003] The integration of space and ground is a multi-domain network, which is suitable for cross-domain request mapping algorithm, but in the current cross-domain request mapping algorithm, the underlying network is usually divided according to different service providers, and the spatial dimension of the underlying network is ignored. When the request is allocated to a certain service provider for mapping, the spatial range of the underlying network is large, which may cause the request to be mapped to a spatial range far away from the access point, the mapping result is too scattered, and the problems of low resource utilization and high latency are caused. SUMMARY

[0004] The purpose of the application is to overcome the above-mentioned deficiencies, and to provide a virtual network mapping method based on request pre-segmentation in the integration of space and ground network, which controls the spatial range of the request mapping result from the inter-domain and intra-domain levels, so as to improve the request acceptance rate and ensure the service quality of the request.

[0005] In order to achieve the above-mentioned purpose, the application comprises the following steps:

[0006] S1, constructing a hierarchical mapping architecture based on a space-time resource tree in the integration of space and ground network, using a hierarchical orchestrator to manage all resources of the hierarchical mapping architecture, and characterizing the resources according to multiple dimensions;

[0007] S2, using the space-time resource tree to represent the multi-dimensional resources required by the request, and comparing with the space-time resource tree in the integration of space and ground network to determine whether request pre-segmentation is needed, if pre-segmentation is needed, entering S3, otherwise entering S4;

[0008] S3, using an improved body mapping label propagation algorithm to pre-segment the request to obtain a request pre-segmentation result;

[0009] S4, the request required multi-dimensional resource allocation to the adapted sub-domain, and adopt multi-dimensional scaling method and k-shell combined way to request the virtual node comprehensive sorting, then according to the sorting results in turn filter out the candidate physical node set of virtual node, and select the highest node selection value of physical node as the current virtual node carrying node mapping, complete mapping, using Dijkstra shortest path algorithm for link mapping, get the final mapping result of the request required multi-dimensional resource.

[0010] The hierarchical mapping architecture based on space-time resource tree in the integrated network of space and earth includes three layers, each layer is managed by an orchestrator, the orchestrator includes a resource representation module, a request pre-segmentation and allocation module and a mapping algorithm module.

[0011] After receiving the mapping request feedback from the sub-domain orchestrator managed by the upper orchestrator, the sub-domain is allocated by the space-time resource tree to meet the resource demand, forming a mapping process from bottom to top feedback and from top to bottom allocation.

[0012] In the hierarchical mapping architecture based on space-time resource tree in the integrated network of space and earth, the orchestrator describes and represents the resource through the dimensions of space, time, type and quantity; the orchestrator describes the node type in the resource through the domain node, time slot node and resource node.

[0013] When the resource changes dynamically, the lower layer orchestrator feeds back the resource dynamic change update to the upper layer orchestrator, and reflects the change of the resource through the real-time change update operation of the space-time resource tree.

[0014] In S3, the specific method of using the improved body mapping label propagation algorithm to pre-segment the request is as follows:

[0015] The resources required by the nodes and links in the request are combined with the high-order features extracted after the body mapping to obtain the voting function of the node to the label of its neighbor node.

[0016] The calculation method of using the improved body mapping label propagation algorithm to pre-segment the request is as follows:

[0017] S vot (u,v)=αP L (u←v)nNum(u,v)+(1-α)P H (u←v)W uv

[0018]

[0019]

[0020] Where node v is a neighboring node of node u, α is a weight factor located between (0,1), nNum(u,v) represents the number of nodes among the neighbors of node u that have the same label as node v, and P L (u←v) represents the degree of acceptability of node u to node v in terms of low-order features, P H (u←v) represents the degree of node acceptability in terms of higher-order features, RE V (e uv ) indicates link e uv The amount of transmission resources, Γ(u) represents the set of neighboring nodes of node u, h u This represents the sum of higher-order weights of the link containing node u. In S4, the method for dynamic node sorting based on multi-dimensional dimensions is as follows:

[0021]

[0022] Among them, elements and These represent the amounts of computational, storage, and observation resources required by the node at time t, respectively. This represents the coefficient of variation for the corresponding resource. This indicates neighbor centrality.

[0023] The calculation method for selecting the physical node with the highest value as the host node of the current virtual node is as follows:

[0024]

[0025] in, For virtual nodes, for The K-shell value, KsNum(G V ) for request G V The total number of K shells in the middle, For nodes The set of neighboring nodes, To host virtual nodes in the current distribution physical nodes, For physical nodes in the underlying network and The shortest path between them, For physical nodes Neighbor centrality in the underlying network subdomain.

[0026] Compared with the prior art, the application designs a hierarchical mapping architecture based on a space-time resource tree in combination with the spatial structure of the underlying network, and completes the mapping process of the request based on this. When the request arrives, if the resource amount of the sub-domain where the request access point is located cannot meet the required resources of the request, the improved motif mapping label propagation algorithm is used to extract the high-order features of the request, and then the label propagation is combined with the low-order features to pre-segment the request, and find a suitable sub-domain for the pre-segmentation result to map. As to the mapping algorithm in the domain, it is mapped based on multi-dimensional node dynamic sorting, fully considers the influence of multiple dimensions of resources on node sorting, and obtains the sorting result of the virtual node through the combination of multi-dimensional scaling method and K-shell, and then selects the physical node with the maximum node selection value as the carrying node of the current virtual node through screening out the candidate physical node set corresponding to the virtual node, to complete the node mapping. And the link mapping is completed through Dijkstra shortest path. The application realizes the spatial controllability of the request mapping result, and also can reduce the remapping of the mapping result required by the time dimension as much as possible, improve the resource utilization rate and the mapping success rate. BRIEF DESCRIPTION OF DRAWINGS

[0027] Figure 1 It is a hierarchical mapping architecture diagram of the application;

[0028] Figure 2 It is a request mapping flowchart under the hierarchical mapping architecture in the application;

[0029] Figure 3 It is a space-time resource tree representation model diagram in the application;

[0030] Figure 4 It is a space-time resource tree representation example diagram of the sub-domain and the request in the application; wherein (a) is a space-time resource tree of the resources owned by the sub-domain, and (b) is a space-time resource tree of the required resources of the request;

[0031] Figure 5 It is a link high and low order weight diagram after motif mapping in the application;

[0032] Figure 6 It is a request pre-segmentation diagram in the application;

[0033] Figure 7 It is a multi-dimensional resource diagram in the integrated space-ground network in the application;

[0034] Figure 8 It is a K-shell solving diagram of the request in the application. DETAILED DESCRIPTION

[0035] The present application will be described in detail below in conjunction with the accompanying drawings and specific embodiments, which are used to explain the present application but not to limit the present application.

[0036] When the present application carries out virtual network request mapping, request pre-segmentation and mapping are needed on the hierarchical mapping architecture after receiving the request, and the implementation of each functional module in the architecture is based on the virtualization of the underlying network. The spatial region of the underlying network is also divided here, and there are two sub-domains in the ground-based network and the space-based network in the figure.

[0037] Step 1, construct a hierarchical mapping architecture based on a space-time resource tree in the integrated space-ground network, use a hierarchical orchestrator for management, and describe the resources in multiple dimensions.

[0038] The hierarchical architecture can be abstracted from the underlying physical network, and a specific example is shown in Figure 1 The architecture is divided into three layers, and each layer has an orchestrator for management. These orchestrators have modules such as resource representation, request pre-segmentation and allocation, and mapping algorithms to implement the mapping of requests. On the basis of the architecture, the request mapping process is as shown in Figure 2 .

[0039] In the resource representation module in the orchestrator, due to the multi-dimensionality of resources in the integrated space-ground network, the number of resources cannot be recorded, but resources need to be described from multiple dimensions. Here, a space-time resource tree model is used to represent the idle resources owned by the sub-domain, Figure 3 An example of using the model to represent the resources owned by the ground-based network sub-domain, the model can be divided into a node tree and a node resource tree, and the main body is a node tree, which can divide resources in terms of spatial range, and the nodes on it represent domain nodes or device nodes. In the leaf nodes of the node tree, a node resource tree is used to represent the resources owned by the sub-domain or the device, and the resources are first divided by time slots, and then described by resource type and quantity. In summary, the space-time resource tree describes resources from multiple dimensions such as space, time, type, and quantity.

[0040] Step 2, use the space-time resource tree to represent the multi-dimensional resources required by the request, and compare it with the space-time resource tree owned by the underlying sub-domain to determine whether request pre-segmentation is needed. If pre-segmentation is needed, go to step 3, otherwise go to step 4;

[0041] When the underlying sub-domain receives a request, it can determine whether the amount of idle resources owned by the sub-domain can meet the amount of resources required by the request through the space-time resource tree model. For example, Figure 4As shown, after the resources are characterized by the model, according to the multi-dimensionality of the resources, it can be determined that the request needs to be pre-segmented at the start time slot. Figure 4 In the example of FIG. 6, no pre-segmentation is needed at the first time slot and the mapping algorithm is directly performed because the number of resources of each type can be satisfied, but at the second time slot, pre-segmentation is needed for the request because there is a resource that cannot be satisfied.

[0042] Step 3, pre-segmenting the request by using the improved motif-based embedding label propagation algorithm to obtain a pre-segmentation result of the request;

[0043] When pre-segmenting the request, because the multiple motifs after pre-segmentation can be mapped to different sub-domains, the correlation between the motifs needs to be considered when mapping, and the correlation within the motifs should be relatively strong and the correlation between the motifs should be relatively weak. The pre-segmentation algorithm in this step is based on the improved motif-based embedding label propagation algorithm (MELP). The MELP algorithm adds a motif mapping part to improve the traditional label propagation algorithm (LP), and solves the problems of unstable pre-segmentation result and unsuitability for weak structural topology of the traditional LP algorithm.

[0044] The MELP algorithm first extracts high-order features of the topology by using the motif structure set in advance to obtain a motif adjacency matrix W, which can be used to represent the size of the high-order weight between nodes. Then, a unique label is initialized for each node, and the label of the node itself is updated by using a voting function of the node on the labels of its neighbor nodes. Finally, when the labels of all nodes no longer change or the maximum number of iterations is reached, the pre-segmentation result can be obtained.

[0045] When the MELP algorithm is applied to the request, the label of the node needs to be initialized first, and then a motif structure of three nodes is used to extract high-order features in the request as the high-order weight of the link. In addition, the number of node and link resources possessed by the request can be used as the low-order features of the request, such as Figure 5 As shown in FIG. 7, there are two weights on the link, which are the required resources of the link and the element value of the motif adjacency matrix, which are the weights corresponding to the high-order and low-order features of the link, respectively. Then, the two high-order and low-order features are used as the consideration factors when the label is propagated, and a voting function of the node on the labels of its neighbor nodes is obtained, which is calculated as shown in formula (1), where node v is a neighbor node of node u, a is a weight factor between 0 and 1, nNum(u,v) represents the number of nodes in the neighbor nodes of node u with the same label as node v, P L(u←v) represents the size of the node acceptance of node u to node v in terms of low-order features, P H (u←v) represents the size of the node acceptance in terms of high-order features. P L (u←v) and P H (u←v) are calculated as shown in equations (2) and (3) respectively, where RE V (e uv ) represents the transmission resource amount of link e uv , Γ(u) represents the neighbor node set of node u, and h u represents the sum of high-order weights of the link where node u is located.

[0046] S vot (u,v) = αP L (u←v)nNum(u,v)+(1-α)P H (u←v)W uv (1)

[0047]

[0048]

[0049] The label propagation is performed by calculating the voting value of each node for the label of its neighbor node, and selecting the label corresponding to the maximum voting value. When the label of the node no longer changes, the label update ends, and the requested pre-partition result can be obtained according to the label corresponding to the node. Figure 6 The schematic diagram of the request pre-partition is shown. According to the pre-partition result, the space-time resource tree of the required resource of each module can be abstracted, and compared with the space-time resource tree of the underlying sub-domain. The average resource utilization rate in the duration T r of the request is calculated as shown in equation (5), and the module with the largest value is allocated to the current sub-domain for mapping.

[0050]

[0051]

[0052] Step 4, the sub-request is allocated to its appropriate sub-domain and mapped based on the mapping method of multi-dimensional node dynamic sorting. The virtual node of the sub-request is sorted by combining the multi-dimensional scaling method and k-shell, and then the candidate physical node set of the virtual node is screened out in sequence according to the sorting result, and the physical node with the highest node selection value is selected as the carrying node of the current virtual node. After the node mapping is completed, the Dijkstra shortest path algorithm is used for link mapping, and the final mapping result of the sub-request can be obtained.

[0053] The two-stage mapping method is adopted, i.e., node mapping and link mapping. In the node mapping stage, the requested virtual node ordering needs to be determined first. According to the space-time resource tree model described in the previous section, the resources in the integrated space-ground system have multiple dimensions such as space, time, type, and quantity. The existing methods often do not consider the multi-dimensionality of resources when sorting nodes, which may lead to problems such as early occupation of critical nodes and scattered mapping results, and cannot be well applied to integrated space-ground networks. As shown in FIG. 8, the changes of resources in multiple dimensions can be reflected. Figure 7

[0054] This application will comprehensively sort the virtual nodes based on the multi-dimensional resource attributes and topology attributes required by the nodes. First, the sorting vector of the node is given as shown in formula (6).

[0055]

[0056] The detailed explanation of each element in the sorting vector c i is as follows:

[0057] 1) The amount of multiple resources required by the node: element represents the amount of calculation, storage, and observation resources required by the node at time t, which can reflect the importance of the node from the type and quantity dimensions of resources.

[0058] 2) Resource dispersion coefficient: element in the formula represents the dispersion coefficient of the corresponding resource, which reflects the dynamic change characteristics of the multiple resources possessed by the node in the time dimension. The smaller the value, the smaller the degree of data dispersion. Taking the calculation resource as an example, the calculation method of the dispersion coefficient is as follows, represents the average value of the calculation resources required by the node in the 0-T time slot.

[0059]

[0060] 3) Neighbor centrality: This index combines the degree of the node and the properties of the neighbor nodes, which can reflect the influence and diffusion ability of the node in the overall network structure. In the sorting vector, it is represented by , and its calculation formula is shown in formula (8), where, represents the weighted degree of node , which is calculated by using the total transmission resources on the link where the node is located, represents the neighbor node set of node , Q ij represents the diffusion influence of the link between node and , and its calculation method is shown in formula (9).​​<q>where denotes the average of all link diffusion influence.

[0061]

[0062]

[0063] Since the ranking of virtual nodes is one-dimensional, it is necessary to reduce the dimension of the ranking vector to reflect the importance of the size relationship between nodes. Here, the multi-dimensional scaling method is used to reduce the dimension of the ranking vector of the virtual node to one-dimensional space for measurement. According to the above explanation of the meaning of each element in the ranking vector, the size of each element value is proportional to the node importance, so the result of dimension reduction is the node importance size relationship from the perspective of resource time, type and quantity and topological properties.

[0064] The first step of the multi-dimensional scaling method is to calculate the distance matrix F ∈ R m×m of the request through the ranking vector of each virtual node, where m is the number of virtual nodes of the request. Here, the Euclidean distance between nodes and is used to construct the elements f ij in the matrix, and the calculation method is shown in equation (10), where p represents the dimension of the ranking vector. The distance matrix F can reflect the similarity of nodes in p-dimensional space, and from its calculation process, it can be seen that the matrix is a real symmetric matrix.

[0065]

[0066] The low-dimensional data obtained after dimension reduction of each node can be represented by the fitting configuration matrix Z ∈ R p ' ×m , where p' is the target dimension, and in the current problem, since the nodes need to be ranked, the value of p' here is 1. The optimal fitting configuration result should be able to keep the distance relationship between the nodes represented consistent with that before dimension reduction, that is, for any two nodes , the corresponding low-dimensional data are Z i , Z j , respectively, and should make the difference between ||Z i - Z j || and f ij minimum, from which the objective function is shown in equation (11).

[0067]

[0068] The above objective can be solved by the cross-correlation matrix B ∈ R m×m of Z, which is related to Z as shown in equation (10),

[0069] B = Z T Z (12)

[0070] By using the multidimensional scaling method, the element b in matrix B can be obtained. ij The calculation formula is shown in (13). After obtaining the cross-correlation matrix B, its eigenvalues ​​are decomposed as shown in formula (14), where Λ=diag(λ1,λ2,…,λ n )(λ1≥λ2≥…≥λ n ), which is the diagonal matrix composed of eigenvalues, and U is the eigenvector matrix. Combining formula (12), it can be seen that Λ 1 / 2 U T Z is calculated.

[0071]

[0072] B = UΛU T =(Λ) 1 / 2 U T ) T (Λ 1 / 2 U T (14)

[0073] The fitted graph matrix Z reflects the distance relationships between nodes before dimensionality reduction. i That is, a virtual node The dimensionality reduction results, when sorted according to the dimensionality reduction values ​​for each node, reflect the importance of nodes in terms of resource time, type, quantity, and topological attributes. However, this importance does not reflect the spatial dimension of node resources. Therefore, the K-shell method is combined here to layer the requests. This method is a coarse-grained layering method based on the overall request structure, which reflects the importance of a node by its position in the request. For a request, the K-shell method iteratively removes nodes of degree k and their associated links. The K-shell value (Ks) of the removed node becomes the current k value, until there are no nodes of degree k in the request. Figure 8 A K-shell request example is provided, showing that nodes with larger Ks values ​​are more important in the request.

[0074] Based on the Ks value of each node, the virtual nodes are sorted by sorting primarily by Ks value and secondarily by dimensionality reduction sorting. By combining the two, the four dimensions of time, space, type and quantity of resources are considered in a comprehensive manner, which can more comprehensively reflect the importance of the nodes.

[0075] After obtaining the ranking results of the virtual nodes, based on the distribution of mapped nodes in the request, the node selection value of the candidate physical nodes for the unmapped virtual nodes is dynamically calculated during the mapping process. The physical node with the largest value is selected for mapping to obtain the most concentrated mapping results possible. Specifically, firstly, for a virtual node, physical nodes that meet its resource requirements are selected based on its multi-dimensional resource needs. Here, a local expansion method is used to narrow down the spatial range of candidate physical nodes. That is, starting from the current mapping distribution, a hierarchical selection is performed in a breadth-first manner. Assuming that there are physical nodes that can meet the resource requirements when expanding to the k-th layer, the nodes in the k and k+1 layers are then selected to obtain the candidate physical node set corresponding to each virtual node. The virtual node ranked first in the ranking results has no mapping distribution as a reference, so the selection range of its candidate physical nodes is the global physical nodes in the subdomain.

[0076] The node selection value of candidate physical nodes is calculated below based on the current mapping distribution and the scalability of physical nodes. Formula (15) gives the physical node selection value. In virtual nodes The formula for calculating the selection value among candidate physical nodes is as follows: express The K-shell value, KsNum(G V ) indicates a request for G V The total number of K shells in the middle, Represents a node The set of neighboring nodes, Indicates the virtual nodes carried in the current distribution. The physical node, if it has not yet been mapped, is... Represents physical nodes in the underlying network. and The shortest path between, if If empty, the value is 0. For physical nodes Neighbor centrality in the underlying network subdomain.

[0077]

[0078] After obtaining the node mapping results, the link mapping is performed using Dijkstra's shortest path algorithm, and finally the requested mapping result can be obtained.

[0079] This invention is not limited to the above embodiments. Based on the technical solutions disclosed in this invention, those skilled in the art can make some substitutions and modifications to some of the technical features without creative effort, and all such substitutions and modifications are within the protection scope of this invention.< / q>

Claims

1. A virtual network mapping method based on request pre-segmentation in an integrated space-ground network, characterized in that, Includes the following steps: S1, construct a hierarchical mapping architecture based on spatiotemporal resource tree in the integrated space-ground network, use a hierarchical orchestrator to manage all resources of the hierarchical mapping architecture, and characterize the resources according to multiple dimensions; S2, Represent the multidimensional resources required by the request using a spatiotemporal resource tree, and compare it with the spatiotemporal resource tree in the space-ground integrated network to determine whether request pre-segmentation is required. If pre-segmentation is required, proceed to S3; otherwise, proceed to S4. S3. The improved motif mapping label propagation algorithm is used to pre-segment the request to obtain the request pre-segmentation result. The specific method is as follows: The resources required by the nodes and links in the request are used as low-order features, which are combined with the high-order features extracted after the motif mapping to obtain the voting function of the node for the label of its neighboring nodes. The calculation method for pre-segmenting requests using the improved motif mapping label propagation algorithm is as follows: Among them, nodes It is a node The neighboring nodes, It is located in Weighting factors between them Represents a node Among the neighboring nodes and nodes The number of nodes with the same label. This indicates that in terms of low-order features, nodes For nodes The size of the node's acceptance level. This indicates the degree of node acceptability in terms of higher-order features. Indicates link The amount of transmission resources, Represents a node The set of neighboring nodes, Represents a node The sum of the higher-order weights of the link in which it is located. For nodes For nodes Voting intensity For nodes With nodes Edge weights between them Indicates link The amount of transmission resources, Represents a node The sum of the higher-order weights of the link in which it is located; S4 allocates the multidimensional resources required by the request to the appropriate subdomains, and uses a combination of multidimensional scaling and k-shell to comprehensively sort the virtual nodes of the request. Then, according to the sorting result, the candidate physical node set of the virtual nodes is selected in turn, and the physical node with the highest node selection value is selected as the carrier node of the current virtual node for mapping. After the mapping is completed, Dijkstra's shortest path algorithm is used to perform link mapping to obtain the final mapping result of the multidimensional resources required by the request.

2. The virtual network mapping method based on request pre-segmentation in an integrated space-ground network according to claim 1, characterized in that, The hierarchical mapping architecture based on spatiotemporal resource trees in the integrated space-ground network consists of three layers, each managed by an orchestrator. The orchestrator includes a resource representation module, a request pre-segmentation and allocation module, and a mapping algorithm module.

3. The virtual network mapping method based on request pre-segmentation in an integrated space-ground network according to claim 2, characterized in that, After receiving a mapping request from the subdomain orchestrator it manages, the higher-level orchestrator allocates a subdomain that can meet its resource requirements through the spatiotemporal resource tree, forming a mapping process of bottom-up feedback and top-down allocation.

4. The virtual network mapping method based on request pre-segmentation in an integrated space-ground network according to claim 2, characterized in that, In the hierarchical mapping architecture based on spatiotemporal resource trees in the integrated space-ground network, the orchestrator describes and represents resources through the dimensions of space, time, type, and quantity; the orchestrator describes the node types in the resources hierarchically through domain nodes, time slot nodes, and resource nodes.

5. The virtual network mapping method based on request pre-segmentation in an integrated space-ground network according to claim 2, characterized in that, When resources change dynamically, the lower-level orchestrator feeds back the dynamic changes to the upper-level orchestrator, reflecting the changes in resources through real-time updates of the spatiotemporal resource tree.

6. The virtual network mapping method based on request pre-segmentation in an integrated space-ground network according to claim 1, characterized in that, In S4, the method for dynamic sorting of nodes based on multi-dimensionality is as follows: in, For virtual nodes Multidimensional comprehensive feature vector, elements These represent the nodes in The amount of computing, storage, and observation resources required at any given moment This represents the coefficient of variation for the corresponding resource. This indicates neighbor centrality.

7. The virtual network mapping method based on request pre-segmentation in an integrated space-ground network according to claim 1, characterized in that, The calculation method for selecting the physical node with the highest value as the host node of the current virtual node is as follows: in, For virtual nodes, for The K-shell value, For the request The total number of K shells in the middle, For nodes The set of neighboring nodes, To host virtual nodes in the current distribution physical nodes, For physical nodes in the underlying network and The shortest path between them, For physical nodes Neighbor centrality in the underlying network subdomain This is the node that hosts the current virtual node.

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