WO2022186808A1

WO2022186808A1 - Method for solving virtual network embedding problem in 5g and beyond networks with deep information maximization using multiple physical network structure

Info

Publication number: WO2022186808A1
Application number: PCT/TR2022/050191
Authority: WO
Inventors: Mustafa Coskun; Vehbi Cagri Gungor; Yesim BAYRAMLI
Original assignee: Havelsan Hava Elektronik San. Ve Tic. A.S.
Priority date: 2021-03-05
Filing date: 2022-03-03
Publication date: 2022-09-09
Also published as: TR202104311A2

Abstract

The present invention relates to a deep learning-based network embedding algorithm that solves the virtual network embedding (VNE) problem for 5G and beyond networks and uses multiple physical network structures. Latent vectors are created by solving it with DGI and matrix states of convergence measures instead of Laplacian matrices in order to solve the VNE problem.

Description

DESCRIPTION

METHOD FOR SOLVING VIRTUAL NETWORK EMBEDDING PROBLEM IN 5G AND BEYOND NETWORKS WITH DEEP INFORMATION MAXIMIZATION USING MULTIPLE PHYSICAL NETWORK STRUCTURE

Technical Field

The present invention relates to a deep learning-based network embedding method that solves the virtual network embedding (VNE) problem for 5G and beyond networks and uses multiple physical network structures.

Prior Art

Network Virtualization is one of the most important technologies that enables the flexible implementation of heterogeneous network applications in shared infrastructures in 5G and beyond technologies.^[1] The most important part of this technology is to embed the virtual network into the physical network as soon as it is requested. This process can be defined as the process of mapping virtual nodes and links with resource demand with physical nodes and ways with limited capacity.^[1] The strategies used in this embedding process are resource utilization; as a result, they play a major role in determining the cost and profit of the network. Network Virtualization is one of the most important technologies that enables the flexible implementation of heterogeneous network applications in 5G and beyond technologies in shared infrastructures as stated above.^[1] The most important part of this technology is to embed the virtual network into the physical network as soon as it is requested. This process can be defined as the process of mapping virtual nodes and links with resource demand with physical nodes and ways with limited capacity.^[1] The strategies used in this embedding process are resource utilization; as a result, they play a major role in determining the cost and profit of the network.

However, most studies face the problem of scalability (inability to solve the problem with modern computers due to NP) with the increase in the size of the network.^[1] Some studies use the pre-processing approach to overcome the scaling problem a little bit and to give embedding algorithms a faster and higher success rate. For example, approaches such as trying to make the embedding option in the subset of the physical network^{[ 1]}, reducing the size of the virtual network^[12], primarily determining the difficulty of the embedding of the virtual network and not running the embedding algorithm at all if it is difficult^[13] can be mentioned.

Even though pre-processing approaches have achieved a partial success, they make the calculation at a bearable speed by considering the resource dimensions associated with both network topology and nodes^[1,4]. In addition, these pre-processing strategies operate on a model-based basis and can not consider the hidden node connections of the system to be resolved on a data-based basis, briefly, the model-based approach may be suitable for one data but does not mean that it will be suitable for another data. Many data-based algorithms from the artificial learning area can be used to leam data here (for example, deep learning), but when the structure under the problem is ultimately a network, classical Euclidean machine learning algorithms do not work here.^[3] Another reason for this is that there is no orientation in the networks as in the pictures.^[3]

Graph Convolutional Network (GCN)^[5], which is a very popular data-based artificial intelligence method in recent years, has started to be used to solve the virtual network embedding problem in this context^[1,14]. The GCN algorithm is a deep learning algorithm presented on networks and leams by using both the topological connection and the features of the latent vector state of each node within the network.^[5] It has become possible to cluster the physical nodes (servers) using source information (e.g., RAM and CPU capacities) and connection information by applying the GCN algorithm to the physical network.^[1,14] The clusters formed make it possible to exclude similar physical nodes from the search space and to focus on more different nodes in this context^11,141. This is only a heuristic solution (since it is NP-hard) to the solution of the Virtual Network Embedding (VNE) problem.^11,141

However, the convergent solution approach of the VNE problem based on GCN^[1,14], which has been applied in recent years, brings along problems related to GCN^[3]. Even though the GCN algorithm is successful, it contains some problems¹¹¹. First, GCN is built on an objective function to recreate the adjancy matrix of the physical network of multiplication of latent vectors when GCN is applied to physical nodes and latent vectors are obtained¹¹¹. This is an objective known as a random walk objective and brings with it many problems with random walk, for example, favoring multi-link nodes^[6] is just one of them^[5]. Secondly, using more than two layers of neural network during the learning phase of GCN using neural networks both prolongs the calculation time and causes label mixing^[7] problem. This prevents GCN from capturing the general structure of the network^[3]. Therefore, the approaches presented to solve the VNE algorithm so far^[1,14] ignore these problems arising from the use of the GCN algorithm.

Various developments have been made regarding the algorithms that exist in the state of the art and presented to solve the VNE problem using Graph Convolutional Network Encoder ^[5].

Different heuristic algorithms or pre-processed algorithms are used to solve this problem convergently since the VNE problem is an NP-hard problem^[2]. It is seen that the versions of classical convolutional neural networks (CNN) on the network are mainly used for heuristic production for Graph Convolutional Networks (GCN) VNE problem with the popularization of deep learning on networks in recent years^[1]. The reason why GCN is used instead of CNN is that CNN cannot express network orientations and GCN specifically develops for networks. The nodes (servers) of the physical network can be expressed as latent vectors using the GCN encoder, the features of the servers, and the server connection information in this context^[1]. That is, the capacity of the servers is referred to as a vector of size d with each server GCN using the capacity of the neighboring servers and network topology information. The vectors obtained for each physical node are clustered by any clustering, for example, K-means algorithm. Finally, clustered servers are used to solve the VNE problem, assuming that the servers in the same cluster should be similar in virtual network embedding. The latent vectors produced by the GCN algorithm used in the solution of the VNE problem clearly play a major role in determining the quality of the solution.

The objective function of the GCN algorithm cannot learn the general structure of the network. Therefore, embedded processing of the physical network should be solved by different techniques that also take into account the overall structure of the physical network, for example Deep Graph InfoMax (DGI). Moreover, the DGI algorithm uses Laplacian matrices during the propagation phase, which again reduces the quality of latent vectors^[3].

The physical network is primarily transferred to the latent vector space in order to solve the VNE problem in convergence in the use of GCN Embedding^[1]. GCN^[5] has started to be used as the main step in the heuristic solution of the VNE problem in recent years, as it can learn both the features of the servers, which are physical nodes, and the topological structure of the network in this embedding process^[1].

GCN tries to learn the embedding process by using two-layer neural networks consisting of Laplacian matrix for a given physical network. Assuming in this context that the capacity of each server (CPU, RAM, etc.) is given as a feature and we keep these features within an X matrix for all servers and the adjacency matrix of the physical network is shown with A. Laplacian operation, which was first used in GCN, is given as follows^[5]:

Here D shows the diagonal matrix showing how many neighbors each server has, and

ensures that the reason for the addition of identity matrix I is that each server

is connected to itself ^[5]. Using the Laplacian operation, which is defined above, the GCN^[5] server performs the embedding process as follows^[1]:

Here, the ReLU non-linear activation function and the weight matrices of the neural

networks determine the size of the number of rows of

The weight matrices

of the neural networks are optimized by solving the following loss function^[5]:

Here, σ displays the sigmoid function.

It is seen that various improvements have been made in some patent documents encountered in the art.

The Chinese patent document CN110233763, which is in the state of the art, mentions a virtual network embedding algorithm and differential learning. It is mentioned in the patent document in question that the algorithm is two-layer and that each node mapping is mapped, taken as a process set and embedded in the process set simulation.

However, the development of the invention in question was needed due to the fact that the methods in the technique are not sufficient against problems such as resource use and scalability in virtual networks and cause other problems.

Objects and Brief Description of the Invention

The object of the present invention is to present another deep learning algorithm instead of GCN [5] in the stage of learning the physical network as latent vectors.

The GCN algorithm uses two-layer neural networks to learn the latent vector state of the physical network. This leads to an increase in learning time. Instead, one-layered neural networks are used with the algorithm of the present invention. This process makes learning time twice as fast.

The similarity matrix of physical nodes, known as the adjacency matrix in the GCN objective function, are tried to recreate, which brings along problems related to random walking. Objective function is used in the universal structure of the latent vectors learned in said invention. It captures the universal physical network structure that GCN cannot capture as a result. Moreover, DGI^[3] uses GCN encoder (Laplacian matrix) in network embedding, which reduces the quality of latent vectors. Thus, the invention is intended to use similarity measure matrices here instead of the Laplacian matrix.

Detailed Description of the Invention

The invention aims to improve scalability resulting from the embedding of a virtual network in a physical network and the slowness caused by virtual network embedding algorithms. A deep learning-based network embedding algorithm has been developed that solves the virtual network embedding (VNE) problem for 5G and beyond networks and uses multiple physical network structures within the scope of this invention. An algorithm focused on convergent and more accurate solution of the virtual network embedding problem^[2], which is used in 5G and beyond shared technologies and classified as NP-hard, has been developed. The main contribution of the invention is the use and forwarding of the DGI^[3] algorithm, which has not been applied to the VNE problem before, in the convergent solution of the VNE problem. Similarly, DGI^[3] algorithm is based on learning an objective function with neural networks, but even though DGI^[3] algorithm uses only a structural similarity of the physical network, latent vectors have been learned with the developed algorithm by considering more than one structural similarity of the physical network. It is presented in the invention that the latent vectors learned will form a more accurate cluster in this way.

Physical Network:

In this invention, the physical network will be given as a network with Here,

N^p shows the set of nodes (servers) within the physical network. Let us assume in this context that the physical network includes the Stane server and we show the set of these servers with Additionally, shows the set of links (physical connections)

between these servers as many as In addition, the capacity

of the amount of resources (RAM and CPU) held by each node server is shown by the R cluster, the capacity of node i is given as and let us give the bandwidth (capacity) of

the Finally, let us show all paths between the two nodes

and the set of physical link between them with Node sources and link

capacity in the physical network are accepted as real numbers in this invention.

Virtual Network:

The virtual network is indicated by and its request is thought to be made on

time, with the set of arrival times in this invention. Here, the number of nodes within the virtual network. Let us assume in this context that there are U nodes in the virtual network and we show them with

Additionally,

shows the set of connections between virtual nodes as many as In addition, let us

define a set of two virtual nodes that are end-to-end connected via link with

the Each virtual node requires

unit resource to complete its task

within the network and each virtual link requires bandwidth of up to for end-to-end

telecommunications in this context. Moreover, let us assume that the virtual network finishes its work in time periods and terminates its request from the physical network. The desired demands in the virtual network are considered to be real numbers as in the physical network.

Using these two network definitions, the Virtual Network Embedding (VNE) problem that is intended to be solved in the invention is given as follows;

VNE Problem:

Each virtual network with an arrival time of t must be either accepted or rejected. The nodes and links in this virtual network must be mapped to the nodes and paths in the physical network that have sufficient resources in order for a virtual network to be accepted. Let's assume that is a binary value indicating the acceptance or rejection of the virtual

network (0 is rejection; 1 is acceptance). The embedding algorithm should decide what value will take without the knowledge of the virtual networks coming after t time in this context. Let us assume that

is the binary value indicating whether the virtual node

is mapped the physical node so that it can give the VNE problem at the node level. Likewise, let

be the binary value indicating whether the

, which is the virtual link, is mapped to the

which is the path between the physical nodes

and

. In light of these definitions, valid virtual network mapping should provide the following mathematical constraints [1]:

Here, the auxiliary function A determines whether the virtual network is as active

as the interval in the t time period. If we list the purposes of the restrictions given by the above equations; equation (1) ensures that the capacities of all source types in each physical node are taken into account, equation (2) guarantees that each virtual link is mapped to the path between at least two physical nodes, and finally equation (3) ensures that the bandwidths on the physical links are used with maximum efficiency. If any of the above restrictions cannot be met, the virtual network is a block. Minimization of this virtual network

blocking is taken as an objective by using effective resource assignment strategy in this invention. More specifically, a minimum amount of physical resource waste is targeted during mapping with this resource assignment strategy. Mathematically, the virtual network acceptance rate can be given as follows [1]:

In addition to the final equation, the profit and cost equations of the algorithm presented to solve the VNE problem can be given as follows [1]:

Here it shows the length of path. In addition, the values of are the

adjustment parameters of the resources with source type r.

Although learning the physical network as latent vectors using GCN^[5] algorithms is a successful approach^[1], it is based on rebuilding the adjacency of the physical network in the purpose function in the equation (9) of the GCN algorithm. However, this approach is the first step of the purpose of random walk^[3] and brings with it problems with random walk, for example, the problem of favoring nodes with high degrees^[6]. In addition, the feature propagation given in equation (8) generally uses two-layer neural networks. The reason for keeping this number of layers limited is to avoid the problem known as label mixing^[7]. However, using a limited number of neural network layers causes the general structure of the physical network not to be fully leamed^[3].

In recent years, an algorithm called Deep Graph Infomax (DGI) has been presented to solve the problems of the GCN^[5] based algorithm stated above^[3]. It is suggested in the developed invention that the embedding process of the physical nodes used in the solution of the VNE problem should be performed with DGI in order to obtain a more accurate result, contrary to the GCN^[1] in the literature. In addition, DGI algorithms use GCN encoder again during the encoder phase, which is an approach to leam the network structure with the Laplacian matrix. Instead, it is presented in the present invention that matrices developed with similarity measures should be used at this stage.

The DGI algorithm is an embedding approach based on the information maximization^[8] used in the objective function of many learning algorithms. Specific to artificial neural networks, DGI performs the embedding process using a stratified neural network as follows:

Here, PReLU shows the parametric ReLU activation function and

shows the trainable neural network weights^[5]. The binary loss function used to train

weights is given as follows:

Here, represents the universal indicator of the whole network, and

shows the M trainable score matrix, which is finally obtained by mixing latent vectors

from equation (10) as rows.

The DGI algorithm^[3] has not yet been used in the literature in the process of producing the latent vector of the physical network created for the heuristic convergence of the VNE problem. It has been proven in the machine learning area that the latent vectors formed by the DGI algorithm^[3] form a much better clustering than the latent vectors created by GCN^[5].^[3] Thus, the invention argues that the expression of the physical network as embedded vectors should be done with DGI algorithms. The reason for this is that DGI algorithms work completely without consulting, capturing the universal structure of physical nodes and walking one step on the physical network in equation (10) (which both removes the random walk operation and reduces the training time of the neural network as it reduces the number of layers of neural networks). However, one-step propagation in equation (10) does not fully capture the universal structure of the network. Instead, it is presented in this invention that the convergence criteria and the encoder stage in equation (10) should be changed.

It is presented in this invention that the encoder process given in equation (10) can be learned with learning techniques^[6] without consulting used in link prediction to learn the physical network as latent vectors. Therefore, the aim of the invention is to maintain the loss function given in the equation (11) in the same way, but to create encoder with the Laplacian convolution matrices used by both DGI^[3] and GCN^[3] algorithms with matrices that measure the similarity of the nodes. Mathematically,

it is desired to create latent vectors with the equation above, (here DGI and GCN use L_SYM instead of C) and it is aimed to make

neural network parameters using equation (11). In this context, the convolution matrices used in equation (12) are given as follows:

(i) Resource Allocation Similarity Measure (RA):

Similar to Adamic-Adar, the measure of similarity in RA is a measure of similarity to punish high-grade nodes^[9] and convolution matrices formed based on the RA measure are given as follows'⁶)

(ii) Hub Depressed Index (HDI): This similarity measure is a node similarity measurement measure constructed as punishment for highly interconnected nodes^[9] according to the one with high grade and convolution matrices formed based on the Node-Based RA measurement are given as follows^[6]:

Here, is to show the matrix containing the same amount of elements as all elements 1 and A in the element-based division N^[6].

(iii) Hub Promoted Index (HPI): To this extent, it is a similar measure to HDI, but it is designed to punish the nodes with less connection^[9] and the convolution matrices formed based on the HPI measurement are given as follows^[6]:

Using the equations given above (13,14,15) as convolution matrices, the physical network can be expressed as latent vectors. However, if the physical network is sparse, using the Laplacian convolution matrix in DGI^[3] gives more accurate results^[3]. In order to overcome this at the same time, is presented in this invention:

The stages of the algorithm that gives the physical network as a latent vector for the adjacency matrix A of a given physical network are listed below.

Deep Graph Infomax Based Embedding Algorithm developed in the invention

Calculation of convolution matrices with equations (7, 13,14 and 15), Calculation of embedding with equation (12) for each structural matrix, Mixing the stunts of the given feature matrices (row -wise shuffle), Calculation of embedding with corrupted features in step 3, as in step 2, Calculation of the universal structure with for embedding

obtained in step 2,

Updating neural network parameters, according to equation (16),

Any clustering algorithm should evaluate these latent vectors in clusters after obtaining the latent vectors of the physical network with the algorithm given above.

The non-patent sources cited throughout the description are as follows;

[1] Habibi, Farzad, Mahdi Dolati, Ahmad Khonsari, and Majid Ghaderi. "Accelerating Virtual Network Embedding with Graph Neural Networks." In 2020 16th International Conference on Network and Service Management (CNSM), pp. 1-9. IEEE, 2020.

[2] E. Amaldi et al., “On the computational complexity of the virtual network embedding problem,” Electron. Notes Discret. Math., vol. 52, pp. 213-220, 2016.

[3]

P. et al. (2019). Deep graph infomax. 7th International Conference on Learning Representations (ICLR 2019).

[4] M. He et al., “DROI: Energy-efficient virtual network embedding algorithm based on dynamic regions of interest,” Comput. Netw., vol. 166, p. 106952, 2020

[5] Kipf, T. N. and Welling, M. (2016b). Variational graph auto -encoders. arXiv preprint arXiv:1611.07308.

[6] Coskun, Mustafa, and Mehmet Koyutürk. "Link prediction in large networks by comparing the global view of nodes in the network." In 2015 IEEE International Conference on Data Mining Workshop (ICDMW), pp. 485-492. IEEE, 2015

[7] Coskun, Mustafa, Burcu Bakir Gungor, and Mehmet Koyuturk. "Expanding Label Sets for Graph Convolutional Networks." arXiv preprint arXiv:1912.09575 (2019).

[8] Linsker, R. (1988). Self-organization in a perceptual network. Computer, 21(3), 105-117. [9] Lii, L. and Zhou, T. (2011). Link prediction in complex networks: A survey. Physica A: statistical mechanics and its applications, 390(6), 1150-1170. [10] Y. Zong et al., “Virtual network embedding for multi -domain heterogeneous converged optical networks: Issues and challenges,” Sensors, vol. 20, no. 9, p. 2655, 2020.

[11] A. Blenk et al., “NeuroViNE: A neural preprocessor for your virtual network embedding algorithm,” in Proc. IEEE INFOCOM, 2018, pp. 405-413.

[12] D. Wang et al., “RLS-VNE: Repeatable large-scale virtual network embedding over substrate nodes,” in Proc. IEEE GLOBECOM, 2019, pp. 1-6

[13] A. Blenk et al., “Boost online virtual network embedding: Using neural networks for admission control,” in Pore. IEEE CNSM, 2016, pp. 10-18

[14] Z. Yan et al., “Automatic virtual network embedding: A deep reinforcement learning approach with graph convolutional networks,” IEEE J. Sel. Areas Commun., vol. 38, no. 6, pp. 1040-1057, 2020.

Claims

1. A deep learning-based network embedding method that solves the virtual network embedding problem for 5G and beyond networks and uses multiple physical network structures, characterized in that it comprises the following steps a. Specific to artificial neural networks, using Deep Graph InfoMax (DGI) embedding method, which can walk one step on the physical network and work without consulting, in a stratified neural network, b. Creating convolution matrices based on the Node-Based Resource Assignment measure, c. Creating convolution matrices based on Hub Depressed Index measurement, d. Creating convolution matrices based on Hub Promoted Index (HPI).

2. A deep learning-based network embedding method that solves the virtual network embedding problem for 5G and beyond networks and uses multiple physical network structures according to claim 1, characterized in that Deep Graph InfoMax (DGI) embedding process comprises the following steps a. Calculation of convolution matrices with equations (7,13,14 and 15), b. Calculation of embedding with equation (12) for each structural matrix, c. Mixing the stunts of the given feature matrices (row-wise shuffle), d. Calculation of embedding with corrupted features in step c, as in step b, e. Calculation of the universal structure with for the

embedding process obtained in step a, f. Updating neural network parameters, according to

equation (16).

3. A deep learning-based network embedding method that solves the virtual network embedding problem for 5G and beyond networks and uses multiple physical network structures according to claim 1, characterized in that it comprises the following a. expressing the DGI embedding process using a stratified neural network as follows:

b. expressing the parametric, activation function and the trainable neural network weights as follows: respectively,

c. expressing the binary loss function used to train neural network weights as follows:

and wherein

is the universal indicator of the whole network,

is obtained by mixing latent vectors from equation (10) as rows, d. creating encoder with the Laplacian convolution matrices with matrices that measure the similarity of the nodes by maintaining the loss function given in the equation (11) and expressing as follows:

and forming latent vectors.

4. A deep learning-based network embedding method that solves the virtual network embedding problem for 5G and beyond networks and uses multiple physical network structures according to claim 1 , characterized in that the convolution matrices formed based on the Node-Based Resource Assignment measure is expressed as follows:

5. A deep learning-based network embedding method that solves the virtual network embedding problem for 5G and beyond networks and uses multiple physical network structures according to claim 1 , characterized in that the convolution matrices formed based on the Hub Depressed Index (HDI) measure is expressed as follows:

6. A deep learning-based network embedding method that solves the virtual network embedding problem for 5G and beyond networks and uses multiple physical network structures according to claim 1, characterized in that the convolution matrices formed based on the Hub Promoted Index (HPI) measure is expressed as follows:

7. A deep learning-based network embedding method that solves the virtual network embedding problem for 5G and beyond networks and uses multiple physical network structures according to claim 1, characterized in that the loss function that enables the optimization of structural information at the same time if the physical network is sparse is expressed as follows: