To address the issues of lagging virtual network function (VNF) migration caused by the dynamic changes in resource requirements in Industrial Internet of Things (IIoT) and the unsatisfactory prediction effect due to the neglect of the connection relationships between nodes in resource requirement prediction, a digital twin(DT)-assisted VNF migration algorithm with spatiotemporal large language model-based resource demand prediction is proposed. Firstly, a large language model-based resource prediction method that combines graph convolutional networks and multi-head self-attention mechanism is introduced to effectively capture spatio-temporal correlations and predict future resource requirements. Next, in order to ensure a deterministic quality of service (QoS) and optimize migration decisions, a DT-assisted VNF migration model composed of energy consumption, latency, and load balancing is constructed, and a joint optimization model for VNF migration and DT re-association aimed at maximizing the long-term utility of the system is established. Finally, a migration algorithm based on heterogeneous multi-agent proximal policy optimization is proposed to solve the VNF migration problem according to the resource requirements predicted by the model. To address the problem of excessive synchronization delays of DT nodes originally associated with nodes after migration, a counterfactual multi-agent algorithm is proposed to solve the problem of DT re-association. Simulation results show that the proposed algorithm improves prediction accuracy, ensures load balancing, and reduces system energy consumption and synchronization delays.

To address the diverse user service requirements in network slicing (NS) and the challenges of synchronization accuracy and low latency in Digital Twin (DT) deployment, this paper proposes a joint optimization strategy for digital twin-based dual-time domain slice resource management and DT deployment in the Internet of Vehicles (IoV). First, a demand-driven slice resource management scheme is introduced to mitigate Quality of Service (QoS) degradation caused by insufficient resource allocation under fluctuating user demands. Network performance indicator weights are dynamically adjusted using demand enhancement factors. Second, to minimize the impact of DT synchronization on resource allocation and address challenges like low latency and delay bias, DT utility is quantified from three perspectives: completeness, load contribution, and resource reliability. Finally, a price incentive mechanism with dynamic load adjustment is designed to balance the supply and demand of DT and service resources. This joint optimization problem is an NP-hard mixed-integer nonlinear problem with dual time-domain coupling, which can be decomposed into utility maximization strategies in different time domains. In the long-time domain, a Q-value-based Deep Transfer Reinforcement Learning (QDTRL) algorithm is used for DT deployment, while in the short-time domain, a Long Short-Term Memory - Multi-Agent Proximal Policy Optimization (LSTM-MAPPO) algorithm is applied for resource allocation and DT synchronization weight adjustment. Simulation results show that, compared to baseline schemes, the proposed strategy achieves higher utility, accelerates convergence, and effectively allocates resources and synchronizes DT.

Escape routing is a critical problem in PCB routing, and its quality dramatically affects the cost of the PCB design. Unlike the traditional escape routing that works mainly for the BGA with unique line width and space, this paper presents a high-performance escape routing algorithm to handle problems with variable design rules and multiple constraints. We first propose a novel obstacle-avoiding method to project pins to the boundary and construct a channel projection graph combined with a channel merging technique to handle complex irregular packages. We then construct a bi-projection graph and propose a matching-based hierarchical sequencing algorithm to consider manual constraints. We perform global routing for each pin/differential pair by congestion-avoiding path initializing and rip-up and reroute path optimizing. Finally, a length-aware detail routing algorithm is developed to optimize the line length while ensuring the differential pair constraints. The experimental results on industrial PCB instances show that our algorithm can achieve 100% routability without violating the design rules and constraints, while two state-of-the-art PCB routers, FreeRouting and Allegro, cannot complete escape routing.

Abstract Medical image colouring techniques enable to colourize grey‐scale medical images for assisting doctors in diagnosis. Benefiting from the non‐linear fitting ability of deep neural network, deep medical image colouring techniques have achieved remarkable results. However, existing methods are still facing content and structure feature leakage, unrealistic colouring and poor scale invariability. Thus, this paper, proposes a Transformer‐based medical image colouring algorithm with long‐term dependency to avoid feature leakage of coloured images. To be specific, this method employs two different Transformer encoders to generate and encode feature sequences for grey‐scale medical images and real human colour slice images, respectively. Then, a novel multi‐layer Transformer decoder is used to stylize grey‐scale map image features based on the real physical colour feature sequences. For colouring images at different scales, we implement content‐ aware positional encoding with scale invariance and propose style‐aware positional encoding strategy to take realistic and physical colour prior into account. Extensive experimental results indicate our method has achieved better colourization effects than recent state‐of‐the‐art medical image colourization methods.

Considering the limited resources, user mobility and unpredictable driving environment in intelligent driving, this paper studies the optimal training efficiency of federated learning for distributed training of collision warning services with the assistance of digital twin (DT). DT is emerging as one of the most promising technologies to make the digital representation of physical components for better prediction, analysis, and optimization of various services in intelligent driving. we first propose a DT-enabled collision warning framework, including physical network layer, digital twin layer, and application layer. Then, for the cooperative training of multi-level warning models combining gate recurrent unit (GRU) and support vector machine (SVM) in the digital twin layer, we propose semi-asynchronous federated learning with adaptive adjustment of parameters (SFLAAP) scheme. We aim at minimizing the training delay of collision warning model by dynamically adjusting the training parameters according to real-time training state and resource conditions of digital space, specifically the local training times and the number of local nodes participating in the aggregation, while ensuring the accuracy of the model. Considering the complexity of the target problem, we propose parameter adjustment algorithm based on asynchronous advantage actor-critic (A3C). Experiments on the classical dataset show high effectiveness of the proposed algorithms. Specifically, SFLAAP can reduce the completion time by about 12% and improve the learning accuracy by about 1%, compared with the state-of-the-art solutions.

Ordered Escape Routing (OER) problem, which is an NP-hard problem, is critical in PCB design. Primary methods based on integer linear programming (ILP) or heuristic algorithms work well on small-scale PCBs with fewer pins. However, when dealing with large-scale instances, the performance of ILP strategies suffers dramatically as the number of variables increases due to time-consuming preprocessing. As for heuristic algorithms, ripping-up and rerouting is adopted to increase resource utilization, which frequently causes time violation. In this paper, we propose an efficient ILP-based routing engine for dense PCB to simultaneously minimize wiring length and runtime, considering the specific routing constraints. By weighting the length, we first model the OER problem as a special network flow problem. Then we separate the non-crossing constraint from typical ILP modeling to reduce the number of integral variables greatly. In addition, considering the congestion of routing resources, the ILP method is proposed to detect congestion. Finally, unlike the traditional schemes that deal with negotiated congestion, our approach works by reducing the local area capacity and then allowing the global automatic optimization of congestion. Compared with the state-of-the-art work, experimental results show that our algorithm can solve cases in larger scale in high routing quality of less length and reduce routing time by 76%.

Escape routing is a critical problem in PCB routing, and its quality greatly affects the PCB design cost. Unlike the traditional escape routing that works mainly for the BGA package with unique line width and space, this paper presents a high-performance escape routing algorithm to handle problems with variable design rules and manual constraints, including variable line widths/spaces, the neck mode of wires, and the pad entry for differential pairs. We first propose a novel obstacle-avoiding method to project pins to the boundary and construct a channel projection graph. We then construct a bi-projection graph and propose a matching-based hierarchical sequencing algorithm to consider manual constraints. We perform global routing for each pin/differential pair by congestion-avoiding path initialization and rip-up and reroute path optimization. Finally, we complete detailed routing in every face, ensuring the wire angle and pad entry constraints. Experimental results show that our algorithm can achieve 100% routability without any design rule violation for all given industrial PCB instances, while two state-of-the-art routers cannot complete routing.

PCB routing becomes time-consuming as the complexity of PCB design increases. Unlike traditional schemes that treat the two essential PCB routing processes separately, namely, escape and bus routing, we consider the continuity between them and present a golden-pin-based routing scheme to find the desired solution with angle and topology constraints. Further, conventional rip-up and reroute methods are often ineffective and inefficient for congestion alleviation and routability optimization. We construct a component graph by modeling components as vertices and applying the minimum weight vertex covering method to improve the routability. A self-adaptable ordering method is presented for escape routing to arrange the pin order on the component boundary, guaranteeing successful bus routing. In addition, escape routing is performed based on a disjoint path method. We construct a dynamic Hanan grid in bus routing and utilize a novel congestion adjustment technique to improve solution quality. Compared with FreeRouting and Allegro, the experiment results show that our algorithm achieves high routability and a significant 90% runtime reduction.

An efficient Intrusion Detection System (IDS) model is essential for the protection of Unmanned Aerial Vehicles (UAVs) networks against network intrusion. However, when designing IDS models using distributed data collected by UAVs, it is crucial to ensure the security and privacy of the data. Moreover, most IDS models only focus on one-time learning and lack continuous learning capabilities. To address this, we present a Federated Continuous Learning framework with a Stacked Broad Learning System (FCL-SBLS) that utilizes Digital Twin Network (DTN) to enable quick and continuous learning on new data. To enhance the efficiency and quality of the IDS model during training and aggregation, we adopt an asynchronous federated learning architecture. Additionally, we introduce a Deep Deterministic Policy Gradient (DDPG)-based UAV selection scheme assisted by DTN to aid in global IDS model aggregation. This approach ensures that the IDS model can effectively and efficiently learn from distributed data while preserving the privacy and security of the data. The presented algorithm is validated using the CIC-IDS2017 dataset, and the simulation results reveal that our algorithm achieves higher efficiency and accuracy than the existing FL scheme.

The edge of the Internet of Things (IoT), which consists of unmanned aerial vehicles (UAVs), is vulnerable to network intrusion because software and wireless connections are used extensively in the IoT. Designing an efficient intrusion detection system (IDS) model is imperative. However, when creating IDS models with distributed data collected by UAVs, it is necessary to take precautions to protect the data’s security and privacy. Furthermore, most of the IDS models are focused on one-time learning but not on continuous learning. To this end, we propose a federated continuous learning framework with a stacked broad learning system (FCL-SBLS) based on the digital twin network (DTN), which can learn and train the IDS model on new data quickly and continuously. In order to improve the efficiency and quality of the IDS model when training and aggregation, we employ an asynchronous federated learning (FL) architecture, and a deep deterministic policy gradient (DDPG)-based UAV selection scheme assisted by DTN is proposed to help the global IDS model aggregation. The presented algorithm is validated using the CIC-IDS2017 data set, and the simulation results reveal that our algorithm achieves higher efficiency and accuracy than the existing FL scheme.

Network slicing (NS) provides customized services to users of the Internet of Things (IoT) by creating logical virtual networks, and NS combined with multiaccess edge computing (MEC) can significantly minimize the latency for delay-sensitive service. Therefore, it is important to research how to employ NS to achieve low latency for delay-sensitive service in MEC-enabled IoT. In this article, we propose a paradigm of dynamic cooperative slicing based on the digital twin network (DTN) to achieve low latency for delay-sensitive service. Specifically, we first build a DTN for the MEC-enabled IoT, and build basic models and function models, including prediction and decision making in DTN. Then, we realize dynamic cooperative slicing through the built basic models and function models. Second, with the assistance of the ubiquitous computing resources in MEC-enabled IoT based on DTN, we construct joint optimization problem of communication resources, computing resources, and collaboration proportion with the objective of ensuring low delay of delay-sensitive service while maximizing the long-term utility of operators. Third, considering that the different MEC servers participating in the cooperation in each time slot lead to different action spaces in different time slots, we propose a deep deterministic policy gradient algorithm with variable action space, called VADDPG, which draws on the idea of action masking and introduces the action adjustor to realize the hard control of action space. Finally, a large number of simulations demonstrate that the proposed algorithm outperforms the benchmark algorithms in terms of both the long-term utility of operators and the delay obtained by slicing.

As a three-layer association of Internet of Things Equipment (IoTE)–network slicing (NS)–base station (BS) in radio access network (RAN) slicing, handoff control, and resource allocation has become an important but complicated issue. In addition, the centralized controller has a difficult grasping the network situation in real time. In view of this, the problem of handoff control in the RAN slicing is investigated in the digital twin network (DTN), with the goal of maximizing the long-term utility about user satisfaction and handoff cost. Then, an improved algorithm based on the actor–critic framework is suggested, which is called HCRA. Specifically, the actor component contains neural networks for handoff control and an optimizer for resource allocation, and then the critic component evaluates the handoff and resource allocation actions of the actor component to guide the optimization of actions in the actor component. The simulation results show that HCRA can obtain better performance than benchmark algorithms.

The Internet of Things (IoT) enables intelligent services varying with the complex and realtime environment to achieve network benefits, where network function virtualization (NFV) can dynamically provide virtualized network functions (VNFs) for IoT devices. In the NFV-enabled IoT architecture, a service function chain (SFC) consists of an ordered set of VNFs. However, the energy consumption of the VNF migration and SFC reconfiguration is one major issue owing to the dynamic characteristic of the IoT network. In this article, we propose a new paradigm digital twin (DT) to create the virtual twin of physical objects in the IoT network, then, we formalize the problem as a mathematical model, which aims to minimize the energy consumption. To this end, we prove this problem is NP-hard and propose an algorithm bidirectional gated recurrent unit (Bi-GRU) based on federated learning to predict the resource requirement. Further more, according to the prediction result, which utilizing the deep reinforcement learning (DRL) algorithm for decision making of the VNF migration. Simulation results show that our proposed method can effectively reduce the number of VNFs to be migrated and economize the energy consumption of the DT IoT network.

Massive and diversified machine type communication (MTC) service is one of the development trends of MTC in Internet of Things (IoT). Meanwhile, realizing network functions virtualization (NFV) is inseparable from reasonable virtual network function (VNF) scheduling and resource allocation. For VNF scheduling and resource allocation of MTC services, recently, deep reinforcement learning (DRL) has become one of the feasible solutions. However, existing DRL solutions have problems of inapplicability to the environment with both discrete and continuous variables, long training, time and nonequilibrium resource allocation. In this article, we first model the end-to-end (E2E) VNF scheduling and resource allocation of core network nodes, links, and access network subcarriers with different strategies, respectively, and propose a compound variable optimization problem aiming at maximizing the net income of the network provider. Then, we propose the mapping scheme of the absolute value of the signum function (ASgn mapping scheme) to simplify the compound variables into continuous variables of the optimization problem, so that the DRL algorithm is applicable. Moreover, we propose a model paralleling multiagent twin delayed deep deterministic (MPMA-TD3) policy gradient algorithm to handle massive services, reduce training time, and action space of agents. Finally, we improve the MPMA-TD3 algorithm to handle diversified services, solve the problem of nonequilibrium resources allocation, and realize the reasonable resource allocation for each service. Simulation results show that the proposed algorithms are better than other algorithms in reward, delay, cost, and training time for massive services. Further, the Improved MPMA-TD3 algorithm has the best service equilibrating ability.

Personalization is one of the primary emerging trends in Industry 4.0 and Beyond. Highly personalized services will present a significant challenge to the existing algorithms for network slicing (NS) and resource allocation, leading to issues, such as nonequilibratory resource allocation, in which some services are sacrificed for the maximum total reward of the algorithm, excessive cost, and slow algorithm convergence. A digital twin network (DTN) is offered as a novel solution to the challenges listed above. By integrating the DTN and IIoT NS, we propose a DTN-assisted industry Internet of Things NS (DTN-IIoT NS) architecture for personalized IIoT services in Industry 4.0 and Beyond. The DTN-IIoT NS architecture consists of three layers, three modules, and two closed loops. On the basis of the aforementioned architecture, we focus on the resource allocation process in DTN-IIoT NS, model the DT-assisted resource allocation for highly personalized IIoT services, propose the service equilibrium rate, and formulate the optimization problem aiming at maximizing the equilibrium rate weighted net profit of network providers. Then, we propose a dual-channel weighted (DCW) Critic network for service equilibrium in DTN-IIoT NS resource allocation and the matching Improved prioritized experience replay (PER) to enhance convergent speed. In addition, we present a distributed DT-assisted DCW-PER multiagent deep deterministic policy gradient (PER-DCW MADDPG) algorithm for the resource allocation process in DTN-IIoT NS. Simulation results indicate that the PER-DCW MADDPG algorithm can produce a better service equilibrium and accelerate the convergence speed of the algorithm.

In modern circuit designs, standard cells are designed with different heights based on the power, area, and other characteristics to address various design requirements. For those cells with different heights, in particular, there are inter-cell diffusion steps if the diffusion heights of neighboring cells are different, called the neighbor diffusion effect (NDE) which has become critical in advanced technology nodes. In this paper, we present a Hamiltonian-path-based mixed-cell-height legalization algorithm for NDE mitigation. We first present a row assignment method considering both cell displacements and diffusion steps to assign cells to their desired rows that meet the power-rail alignment constraints. Then, we propose a Hamiltonian-path-based diffusion-step reduction method to effectively reduce the NDE violations while preserving the global placement solution. Particularly, we develop a 2-approximation algorithm to find a minimum weight Hamiltonian path connecting two vertices, and a 1.5-approximation algorithm to find a minimum weight Hamiltonian path with a specified end vertex. Finally, we present an NDE-aware legalization method with design compaction to resolve overlaps and NDE violations. Experimental results show that our algorithm can resolve all NDE violations without any area overhead in reasonable runtime.

With the development of the technology, the wireless systems are becoming more heterogeneous with the introduction of various power nodes including femtocells, relays, or distributed antennas. Among the research of wireless network performance, the meta distribution of the signal-to-interference ratio (SIR) has attracted significant attention. Compared to the standard success (coverage) probability, the meta distribution provides much more fine-grained information about the network performance. In this paper, we analyze the meta distribution of the SIR in the multi-tier heterogeneous and hybrid networks, where each tier is based on a homogeneous independent Poisson point process model. For the open tiers (the users can associate with any tier) and the closed tiers (the users can only associate with a certain tier), we study the b th moment of the conditional success probability for the typical user and give the beta approximation of the meta distribution from analysis and simulations. Furthermore, we analyze the per-link rate control for open tiers and closed tiers, which answers the question: “how to set the SIR threshold to meet a target reliability?”. We give the approximate value of the SIR threshold to meet a target reliability and show how the value is related to the path loss exponent and densities.

Abstract An edge set S is a k‐restricted edge cut of a connected graph G if G‐S is no longer connected and every component of G‐S has at least k vertices. The k‐restricted edge connectivity of G, denoted by λk(G), is the cardinality of a minimum k‐restricted edge cut. A graph G with λk(G) = ξk(G) is called λk‐optimal, where ξk(G) = min{∣U,Ū∣ ∣ U ⊂ V(G),∣U∣ = k and GU is connected}, ∣U,Ū∣ is the number of edges between U and Ū, GU is the subgraph of G induced by U. In this article, we give a sufficient condition for a graph to be λk‐optimal: for any integer k ≥ 3, every graph G with girth g ≥ 5, minimum degree δ ≥ k, and diameter D ≤ g ‐ 4 when g is even and D ≤ g ‐ 3 when g is odd is λk‐optimal. Furthermore, if δ ≥ 2k ‐ 3, the diameter condition can be relaxed a little to D ≤ g ‐ 3 no matter whether g is even or odd. This generalizes a result of Balbuena et al. [Sufficient conditions for λ′‐optimality in graphs with girth g, J Graph Theory 52 (2006) 73–86], and improves a result of Fàbrega and Fiol in a sense [On the extraconnectivity of graphs, Discrete Math 155 (1996) 49–57]. © 2009 Wiley Periodicals, Inc. NETWORKS, 2010