Network Embedding Problem Research Articles

Learning dynamic embeddings for temporal attributed networks

Learning low-dimensional representations for networks has attracted considerable research interest due to the ever-increasing volume and variety of network-based information. It becomes especially important and challenging for temporal networks whose nodes and attributes evolve as time changes. To address the problem of temporal network embedding, we propose a novel Dynamic Bayesian Temporal Network Embedding (DBTNE) method that adopts a probabilistic framework and represents network embeddings as Gaussian distributions for learning effective embeddings for temporal networks. Unlike the existing temporal network embedding methods that learn dynamic embeddings only for nodes, our DBTNE jointly learns the dynamic embeddings of both nodes and attributes in temporal attributed networks for effectively capturing the similarities among them, which greatly facilitates attribute-related learning tasks such as link prediction, object classification and user profiling. In addition, we model the temporal dynamics of both nodes and attributes with neural ordinary differential equations, which supports effective and efficient capture of long-range dependencies among embeddings at different timestamps. Extensive experimental results on real-world temporal networks demonstrate that our DBTNE achieves better performance than popular state-of-the-art methods, including DeepWalk, Node2Vec, CAN, HTNE, M2DNE, MTSN, Dane-ATT, for typical graph learning tasks, such as dynamic link prediction and node classification.

Towards learning-based energy-efficient online coordinated virtual network embedding framework

Network virtualization is a highly effective technology for resource sharing within data centers, enabling the coexistence of multiple heterogeneous virtual networks in a shared substrate network, thus achieving resource multiplexing. The efficient embedding of a virtual network onto a substrate network, known as the virtual network embedding (VNE) problem, has been proven to be NP-hard. In response to this challenge, this paper introduces a novel method, named PPO-VNE, which leverages deep reinforcement learning for virtual network embedding. PPO-VNE employs the Proximal Policy Optimization (PPO) algorithm to generate policies and efficiently coordinate node and link mapping. Furthermore, it adopts a hybrid feature extraction approach that combines handcrafted features with features extracted using graph convolutional networks. The proposed reward function takes multiple objectives into account, guiding the learning process. We implemented a prototype of PPO-VNE and conducted experiments based on the simulation environment, in which the substrate network has 100 nodes, with a probability of 0.1 generating edges between any two node, and eventually there will be about 500 physical links. We evaluate the performance of our PPO-VNE approach from the perspective of overall acceptance rate, overall revenue, revenue-to-cost ratio, maximum energy consumption per unit time and revenue-energy consumption coefficient. Comprehensive simulation results in different scenarios show that our PPO-VNE approach achieves the superior performance on most metrics compared with the existing state-of-the-art approaches, where the overall acceptance rate, overall revenue, revenue-energy consumption coefficient are increased by up to 6.4%, 21.3% and 41.4%, respectively, and the maximum energy consumption per unit time are reduced by up to 22.1%.

Artificial algae optimization for Virtual Network Embedding problems in 5G network slicing scenarios

Network slicing enables diverse scenarios within The Fifth Generation of Cellular System (5G) and beyond systems. Mapping virtual networks to their physical counterparts, known as the Virtual Network Embedding (VNE) problem, is challenging with mathematical complexities. While Linear Programming (LP) approaches can address the VNE problem, they may prove impractical due to the execution time required to obtain optimal solutions. Furthermore, meta-heuristic algorithms offer a promising alternative in balancing solution optimality and execution time. In this study, we propose the Artificial Algae Algorithm (AAA) as a solution for the VNE problem in network slicing scenarios specific to 5G. We compare the performance of AAA with other commonly used meta-heuristics, including Genetic Algorithm (GA), Differential Evolution (DE), and Particle Swarm Optimization (PSO). Since the evolutionary process of AAA consistently operates in three random dimensions, irrespective of the problem’s dimensionality, the runtime performance of AAA remains unaffected by the number of virtual nodes, yielding execution times up to ten times faster than DE and PSO when considering 30 nodes. In that scenario, the proposed approach with AAA presented an improvement of more than 60% compared to DE and PSO in an execution time ten times lower.

Spatio-temporal fragmentation-aware time-varying service provisioning in computing power networks based on model-assisted reinforcement learning

Widespread application of AI with high computing requirements has promoted the rapid development of cloud and edge computing. Ubiquitous computing resources need to be interconnected through high-performance IP and optical networks. Computing power networks (CPNs) have been studied as an IP/optical cross-layer architecture to provide on-demand computing services. The service provisioning in CPNs can be modeled as a virtual optical network embedding problem; however, the time-varying characteristics of service requirements increase the complexity. In particular, there can be stranded computing or bandwidth resources that are isolated in the spatio-temporal dimension and therefore difficult for other requests to utilize. This phenomenon is referred to as spatio-temporal resource fragmentation, which will lead to inefficient use of resources and higher energy consumption. To meet the time-varying requirements and achieve an energy-efficient CPN, in this paper, we first analyze the main reason for spatio-temporal resource fragmentation and excess energy consumption in cross-layer CPNs, which is the mismatched embedding scheme and the inappropriate scheduling order. Therefore, an auxiliary-graph-model-assisted edge-featured graph-attention-network-enabled DRL algorithm, DeepDefrag, is studied to solve the problem. Its core highlight is co-optimizing the scheduling and embedding of time-varying virtual networks along with the awareness of resource fragmentation. In addition, an integer linear programming algorithm is developed to determine the performance bounds. We validate DeepDefrag through a series of ablation studies and comparison algorithms under different numbers of requests. The results show that DeepDefrag can achieve >26.4% lower energy consumption for CPNs compared with the DRL-based baseline. Moreover, it is shown to generalize well across requests and networks.

E2DNE: Energy Efficient Dynamic Network Embedding in Virtualized Wireless Sensor Networks

Efficient utilization of resources is an important challenge in traditional non-virtualized Wireless Sensor Networks (WSNs), as the applications are embedded in the sensors, precluding the sensor nodes from being re-used by other applications. Inefficient utilization of resources results in high deployment and maintenance costs. Virtualization is a promising technology that allows multiple sensing tasks from diverse applications to be executed on the same deployed WSNs concurrently. However, given that the WSN sensors are constrained with limited energy, the allocations of physical and virtual resources to the applications in an efficient manner becomes a challenge, especially for mission-critical, delay-sensitive applications. In this paper, we address the problem of virtual network embedding in virtualized WSNs, aiming at minimizing the overall energy consumption while considering the end-to-end latency and bandwidth consumption as the service level agreement (SLA) constraints. We propose our Dynamic Network Embedding (DNE) heuristic for large-scale problem instants. The results reveal that our proposed heuristic leads to close-to-optimal solutions with satisfactory execution time. Our results indicate that the proposed heuristic achieves up to an 18% optimality gap in energy consumption in the small-scale scenario, and outperforms the existing benchmark by up to 58% in the large-scale scenario.

Reinforcement Learning-Based Slice Isolation Against DDoS Attacks in Beyond 5G Networks

Network slicing in 5G networks can be modeled as a Virtual Network Embedding (VNE) problem, wherein the slice requests must be efficiently mapped on the core network. This process faces two major challenges: covering the maximum number of requests and providing slice isolation. Slice isolation is a mechanism for protecting the slices against Distributed Denial of Service (DDoS) attacks. To overcome these two challenges, we have proposed a novel actor-critic Reinforcement Learning (RL) model, called Slice Isolation-based Reinforcement Learning (SIRL), using five optimal graph features to create the problem environment, the form of which is changed based on a ranking scheme. The ranking procedure reduces the dimension of the features and improves learning performance. We evaluated SIRL by comparing it against four non-RL and nine state-of-the-art RL models. The average results show that the ratio of the covered requests and the damage caused by a DDoS attack of SIRL is 54% higher and 23% lower than that of the other models, respectively. It also has an acceptable learning performance and generality, regarding the reported results that show SIRL agents trained and tested with different networks outperform the other agents by 97%.

5G in healthcare: Matching game-empowered intelligent medical network slicing

Improving the healthcare system is imperative for increasing efficiency and reducing costs. The rapid adoption of Internet of Medical Things (IoMT) has facilitated a broad range of healthcare applications and services, from real-time and critical care monitoring to telemedicine. These services typically have highly distinct quality of service (QoS) requirement for communication networks and thus cannot be served with a uniform network. In such a context, network slicing technologies in 5G can be employed to create virtually independent and customized communication networks for these use cases to meet their QoS requirement. In this wok, we model network slicing for healthcare services as a virtual network embedding (VNE) problem and propose a two-sided matching theory-based virtual network embedding (MT-VNE) solution. In MT-VNE, four novel preference indexes are devised to construct differential preference lists. The deferred acceptance and modified shortest path-based algorithms are utilized to perform the virtual node and link mapping, respectively. Extensive simulations demonstrate that MT-VNE outperforms other baselines in terms of accepting more healthcare services and effectively utilizing physical network resources. Moreover, MT-VNE also significantly reduces service embedding time.

Priority-Based Search for the Virtual Network Embedding Problem

The Virtual Network Embedding (VNE) problem is a constrained optimization problem. It arises in the context of allocating resources on heterogeneous physical networks to provide end-to-end computing services. In this paper, we introduce a new solver, called VNE-PBS, that uses priority-based search (PBS) for solving the VNE problem. VNE-PBS uses a prioritized heuristic search algorithm that explores the space of all possible priority orderings using a systematic depth-first search. The solver is inspired by the success of PBS for the Multi-Agent Path Finding (MAPF) problem and the similarities between the VNE and MAPF problems. We show that VNE-PBS significantly outperforms competing methods on various benchmark instances for both the offline and online versions of the VNE problem.

HA-D3QN: Embedding virtual private cloud in cloud data centers with heuristic assisted deep reinforcement learning

The virtual network embedding problem is embedding virtual networks (VNs) in a substrate network so that revenue or accept ratio is maximized. Previous study usually assumes disclosed communication demand among the virtual nodes in a VN, mismatching real-world cloud computing scenarios. In this paper, we propose a new VN abstraction based on the widely used Virtual Private Cloud model, where internal communication demand is unknown to cloud providers. In contrast with the majority of existing research, we allow the co-location of the virtual nodes belonging to the same VN, and introduce the concept of switching capacity for practical resource reservation. We categorize the substrate resources in cloud data centers into additive and non-additive for the first time, and devise our algorithms accordingly. After formulating the problem, we propose a solution framework named HA-D3QN (Heuristic Assisted Dueling Double Deep Q Network). Essentially, HA-D3QN selects the best responses to different system states by combining the D3QN deep reinforcement learning structure and the candidate actions, which are generated by our proposed heuristic algorithms for addressing the exponentially large action space. Finally, we conduct extensive simulation experiments, the results of which verify the effectiveness of our approach.

Deep Reinforcement Learning Algorithm for Latency-Oriented IIoT Resource Orchestration

Due to geographical factors and resource constraints, the traditional Internet architecture cannot meet the needs of the space–air–ground-integrated network (SAGIN) resource layout in the Industrial Internet of Things (IIoT) service. How to arrange network resources in SAGIN quickly and efficiently to meet the quality of service requirements of users has become a hot research topic in the industry. Based on the characteristics of SAGIN with multiple network segments, we convert the resource scheduling problem of SAGIN into a multidomain virtual network embedding (VNE) problem. This article proposes a latency-sensitive VNE algorithm based on deep reinforcement learning (DDRL-VNE) in the SAGIN environment. Unlike traditional latency optimization algorithms, we consider the effect of traffic size and hop count on latency when evaluating latency. We constructed a learning agent composed of a five-layer policy network and extracted a feature matrix as its training environment based on the network attributes of SAGIN. The node embedding is completed according to the probability that each node is embedded in the training, and then the breadth-first search strategy is used to complete the link embedding. The experimental results effectively illustrate the effectiveness of the algorithm in the SAGIN resource allocation problem.

Graph Convolutional Network Aided Virtual Network Embedding for Internet of Thing

The past few years have seen the dramatic adoption of the Internet of Things (IoT) in everyday life, from manufacturing to healthcare. With the emergence of various new Internet of Things applications, it is a challenging problem to meet the different QoS requirements of Internet of Things applications in shared substrate networks. Recently, Network Virtualization (NV) has attracted a large amount of attention from academia and industry. NV enables multiple virtual networks to coexist on the same substrate network, thus providing IoT users with customized end-to-end services. The main challenge of NV is the Virtual Network Embedding (VNE) problem, which refers to embed different virtual networks into one substrate network. Inspired by the recent success of graph convolutional network (GCN) in graph structured data processing, in this paper, we propose a GCN aided VNE algorithm. The GCN can extract high-order spatial structure information among substrate nodes through the convolution kernel. Considering that the training data of VNE has no label, we introduce the policy gradient algorithm to optimize the GCN model. In addition, three evaluation metrics are designed to evaluate the performance of the network embedding policy. Some simulations are implemented to evaluate our proposed algorithm in comparison to the other state-of-the-art solutions.

Optimal Embedding of Heterogeneous RAN Slices for Secure and Technology-Agnostic RANaaS

A key challenge related to Radio Access Network (RAN) slicing is deciding how to efficiently map radio resources from the physical radio to realise RAN slices, known as the virtual wireless network embedding problem. To the best of our knowledge, this is the first paper to model and derive an analytical solution for embedding heterogeneous RAN slices with different waveforms, numerologies and Radio Access Technologies (RATs) with resources isolated down to the Physical (PHY) layer, ultimately enabling secure technology-agnostic RAN as a Service (RANaaS). First, we assess how current virtual wireless network embedding solutions model the allocation of radio resources to realise RAN slices. Then, we propose a graph-based model for embedding heterogeneous RAN slices that considers the guard bands required to ensure isolation in the frequency domain. This approach is transparent to the type and granularity of radio resources of each RAN slice, and can be extended to support RAN slices with new waveforms, numerologies and RATs. Next, we introduce a resource management optimisation problem solved at the Network Provider (NP) to determine the optimal embedding of RAN slices that maximises the total useful bandwidth occupied by tenants; and we propose three different heuristic algorithms to obtain solutions in near real-time. We compare their performance against the analytical solution using different metrics, and our results show that the best heuristic depends on the NP’s business model, e.g., using the Greedy Algorithm (GA) to increase resource utilisation or the Nearest Neighbour Algorithm (NNA) to increase the number of allocated RAN slices.

Web Service Network Embedding Based on Link Prediction and Convolutional Learning

Extensive efforts have been applied to develop efficient feature extraction algorithms, which aim to achieve optimal results in many fundamental tasks such as Web-based software service clustering, recommendation and composition. However, one common issue for existing methods is that mined features are problem dependent, causing poor generalization ability across different applications. Recent studies show that we can represent networked data (e.g., citation networks and social networks) as low-dimensional vectors with rich structure and content information preserved, which can then greatly facilitate many downstream tasks such as classification and clustering. In this article, we focus on the problem of Web service network embedding, which aims to learn low-dimensional vectors to represent services by encoding both Mashup-API composition structure and service functional content. We first propose a novel probabilistic topic model to predict potential links between Mashups and APIs in the service network. Then, we develop a Service Graph Convolutional Network (Service-GCN) to learn vector representations of services, where each service (e.g., Mashup or API) forms its representation through message passing between neighborhood services over the network. We evaluate the network embedding quality on two real-world datasets for downstream classification and clustering tasks. Experimental results show that the average performance of our method improves 20.7 percent (Micro-F1) in service classification and 19.0 percent (Accuracy) in Mashup clustering compared to the state-of-the-art, which verified the effectiveness of the proposed approach for learning vector representations of Web services.

Repeatable Multi-Dimensional Virtual Network Embedding in Cloud Service Platform

Virtual network embedding (VNE) can effectively deploy virtual networks (VNs) onto shared substrate network (SN) resources. However, with the consistent changing scalability and diversity demands of VNs, traditional VNE methods prove to be a challenging task for current cloud service platforms. Thus, we model a repeatable multi-dimensional virtual network embedding (RMD-VNE) problem for implementing multi-dimensional virtual networks (MD-VNs) that involves real servers, virtual machines, containers, and network simulators. The MD-VN is preprocessed and embedded via a heuristic method denoted as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ReMiDvne</i> . Following its transformation for the containers and simulation networks, the MD-VN topology undergoes a process of coarsening, partitioning, and uncoarsening. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ReMiDvne</i> then applies a topology-aware repeatable embedding solution to complete the embedding stage. Experimental results demonstrate that <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ReMiDvne</i> outperforms seven baseline approaches through small-, 1,000- and 10,000-scale VNE simulation experiments. Remarkably, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ReMiDvne</i> improves the average rates of acceptance ratio, revenue, and revenue-cost ratio by up to 40.45, 40.45, and 299.03 percent, respectively, and reduces the average rate of cost by up to 64.16 percent. Furthermore, real-world VNE experiments are conducted based on the OpenStack platform. The results reveal the ability of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ReMiDvne</i> to efficiently reduce communication costs by up to 45.93 and 63.43 percent for download and upload, respectively.

Monkey Business: Reinforcement learning meets neighborhood search for Virtual Network Embedding

In this article, we consider the Virtual Network Embedding (VNE) problem for 5G networks slicing. This problem requires to allocate multiple Virtual Networks (VN) on a substrate virtualized physical network while maximizing among others, resource utilization, maximum number of placed VNs and network operator’s benefit. We solve the online version of the problem where slices arrive over time. Inspired by the Nested Rollout Policy Adaptation (NRPA) algorithm, a variant of the well known Monte Carlo Tree Search (MCTS) that learns how to perform good simulations over time, we propose a new algorithm that we call Neighborhood Enhanced Policy Adaptation (NEPA). The key feature of our algorithm is to observe NRPA cannot exploit knowledge acquired in one branch of the state tree for another one which starts differently. NEPA learns by combining NRPA with Neighborhood Search in a frugal manner which improves only promising solutions while keeping the running time low. We call this technique a monkey business because it comes down to jumping from one interesting branch to the other, similar to how monkeys jump from tree to tree instead of going down everytime. NEPA achieves better results in terms of acceptance ratio and revenue-to-cost ratio compared to other state-of-the-art algorithms, both on real and synthetic topologies.

Application of Meta-Heuristics in 5G Network Slicing: A Systematic Review of the Literature.

Network slicing is a vital component of the 5G system to support diverse network scenarios, creating virtual networks (slices) by mapping virtual network requests to real networks. The mapping is an arduous computing process, mathematically studied and known as the Virtual Network Embedding (VNE) problem, and its complexity is NP-Hard. The mapping process is oriented to respect the QoS demands from the virtual network requests and the available resources in the physical-substrate infrastructure. Meta-heuristic approaches are a suitable way to solve the VNE problems because of their capacity to escape from the local optimum and adapt the solution search to complex networks; these abilities are essential in 5G networks scenarios. This article presents a systematic review of meta-heuristics organized by application, development and problem-solving approaches to VNE. It also provides the standard parameters to model the infrastructure and virtual network requests to simulate network slicing as a service. Finally, our work proposes some future research based on the discovered gaps.

Conflict-Based Search for the Virtual Network Embedding Problem

In emerging network virtualization architectures, service providers will be able to create many heterogeneous virtual networks and offer customized end-to-end services by leasing shared resources from infrastructure providers. The Virtual Network Embedding (VNE) problem is central to such technology. It involves the proper allocation of CPU and bandwidth resources available in a physical substrate network to meet the demands of multiple virtual networks. Combinatorially, the VNE problem is a problem in resource management that is NP-hard to solve. In this paper, we present a novel version of the Conflict-Based Search (CBS) algorithm for solving the VNE problem. Our approach, called VNE-CBS, is inspired by the success of the CBS framework in the Multi-Agent Path Finding domain. We successfully address the unique challenges in applying the CBS framework to the VNE problem, and, in doing so, we pave the way for overcoming a crucial issue in Internet ossification via heuristic search methods. On the theoretical front, we show that, unlike many existing algorithms, our algorithm is complete and optimal. On the experimental front, we show that our algorithm significantly outperforms other state-of-the-art methods on various benchmark instances for both the offline and online versions of the VNE problem.

Resource Fragmentation-Aware Embedding in Dynamic Network Virtualization Environments

In network virtualization environments, with random arrival and departure of virtual network requests, there exist some resources (i.e., link resources and node resources) isolated from others in substrate networks. This phenomenon is referred to as resource fragmentation. In this paper, we attempt to improve the resource utilization efficiency by avoiding resource fragmentation in substrate networks. First and most importantly, we define a new metric called resource fragmentation degree (RFD) to quantitatively measure the status of resource fragmentation at substrate nodes and links. The basic idea of RFD is that the resource availability of a node (or a link) is determined by the residual link and node resources around the node (or the link). Based on the definition of RFD, we formulate the virtual network embedding (VNE) problem as a mixed integer programming problem with consideration of the cost of resource fragmentation. Then, an online VNE algorithm with consideration of RFD (VNERFD) is proposed to solve the problem, which is performed according to the current resource status of substrate networks and virtual network requests. To reduce accumulated fragmented resources produced by dynamic arrival and departure of virtual network requests, a heuristic virtual network reconfiguration algorithm based on RFD (VNR-RFD) is proposed. Simulation results show that VNE-RFD and VNR-RFD can effectively reduce fragmented resources and thus embed more virtual networks into substrate networks.

Single-particle optimization for network embedding preserving both local and global information

As an emerging topic, network embedding aims to convert the complicated network information into a low-dimensional vector space that largely preserves the network topology and effectively benefits various network tasks. Most existing methods mainly focus on the sketchy preservation of local or global network information, which greatly limits their application scenarios. In this paper, we propose a single-particle optimization algorithm for network embedding problems (SPO-NE) to carefully preserve both the local properties of nodes and the global community structure of networks. Based on the evolutionary scheme of particle swarm optimization, SPO-NE innovatively uses a single particle with two well-designed strategies for optimization. The multi-level learning strategy is devoted to comprehensively saving the local properties of nodes from three aspects of similarity, degree, and community, while the transfer strategy serves to help the nodes located at the community boundary to obtain better community labels. In experiments, SPO-NE is compared with several state-of-the-art baselines on both real-world and synthetic networks. The results indicate the superiority of SPO-NE on various network tasks. Specifically, SPO-NE can outperform the best baselines by over 10% on five datasets in community detection. With only 10% training samples in node classification, SPO-NE can improve the best baselines by 7–10% on five datasets.

Space-Air-Ground Integrated Multi-Domain Network Resource Orchestration Based on Virtual Network Architecture: A DRL Method

Traditional ground wireless communication networks cannot provide high-quality services for artificial intelligence (AI) applications such as intelligent transportation systems (ITS) due to deployment, coverage and capacity issues. The space-air-ground integrated network (SAGIN) has become a research focus in the industry. Compared with traditional wireless communication networks, SAGIN is more flexible and reliable, and it has wider coverage and higher quality of seamless connection. However, due to its inherent heterogeneity, time-varying and self-organizing characteristics, the deployment and use of SAGIN still faces huge challenges, among which the orchestration of heterogeneous resources is a key issue. Based on virtual network architecture and deep reinforcement learning (DRL), we model SAGIN&#x2019;s heterogeneous resource orchestration as a multi-domain virtual network embedding (VNE) problem, and propose a SAGIN cross-domain VNE algorithm. We model the different network segments of SAGIN, and set the network attributes according to the actual situation of SAGIN and user needs. In DRL, the agent is acted by a five-layer policy network. We build a feature matrix based on network attributes extracted from SAGIN and use it as the agent training environment. Through training, the probability of each underlying node being embedded can be derived. In test phase, we complete the embedding process of virtual nodes and links in turn based on this probability. Finally, we verify the effectiveness of the algorithm from both training and testing.