Fault-tolerant Network Research Articles

Structure connectivity of folded cross cubes

Abstract Connectivity is an important parameter to measure fault-tolerance of networks. As a generalization, structure connectivity and substructure connectivity of networks were proposed. For connected graphs $G$ and $H$, the $H$-structure connectivity $\kappa (G; H)$ (resp. $H$-substructure connectivity $\kappa ^{s}(G; H)$) of $G$ is the minimum cardinality of a set of subgraphs $\mathcal{F}$ of $G$ that each is isomorphic to $H$ (resp. a connected subgraph of $H$) such that $G-\mathcal{F}$ is disconnected or the singleton. $n$-dimensional folded cross cube, $FCQ_{n}$, is a network obtained by adding edges to $n$-dimensional cross cubes. In this paper, we study star, path, and cycle structure connectivity and substructure connectivity of $FCQ_{n}$, where $n\geq 8$. For star ($K_{1,m}$) structure, we get that $\kappa (FCQ_{n}; K_{1, m})=\kappa ^{s}(FCQ_{n}; K_{1, m})=\lceil \frac{n + 1}{2} \rceil $ for $2 \leq m \leq \frac{n}{2}$. For path ($P_{k}$) structure, we show that for $3\leq k\leq n+1$, if $k$ is odd, then $\kappa (FCQ_{n}; P_{k})=\kappa ^{s}(FCQ_{n}; P_{k})=\lceil \frac{2(n + 1)}{k+1}\rceil $; if $k$ is even, then $\kappa (FCQ_{n}; P_{k})=\kappa ^{s}(FCQ_{n}; P_{k})=\lceil \frac{2(n + 1)} {k}\rceil $. For cycle ($C_{k}$) structure, we prove that $\kappa ^(FCQ_{n}; C_{k})=\kappa ^{s}(FCQ_{n}; P_{k})$. Further, we calculate $\kappa ^(FCQ_{n}; C_{2k-1})=\lceil \frac{n+1}{k-1} \rceil $ for $4 \leq k \leq n+2$ and $C_{2k}$-structure connectivity of $FCQ_{n}$ is $\lfloor \frac{n+1}{k} \rfloor +1$ for $6 \leq k\leq n + 1$ and even $k$.

Bayesian Machine Learning Meets Formal Methods: An Application to Spatio-Temporal Data

We propose an interdisciplinary framework that combines Bayesian predictive inference, a well-established tool in machine learning, with formal methods, rooted in the computer science community. Bayesian predictive inference allows for coherently incorporating uncertainty about unknown quantities by making use of methods or models that produce predictive distributions, which in turn inform decision problems. By formalizing these decision problems into properties with the help of spatio-temporal logic, we can formulate and predict how likely such properties are to be satisfied in the future at a certain location. Moreover, we can leverage our methodology to evaluate and compare models directly on their ability to predict the satisfaction of application-driven properties. The approach is illustrated in an urban mobility application, where the crowdedness in the center of Milan is proxied by aggregated mobile phone traffic data. We specify several desirable spatio-temporal properties related to city crowdedness such as a fault-tolerant network or the reachability of hospitals. After verifying these properties on draws from the posterior predictive distributions, we compare several spatio-temporal Bayesian models based on their overall and property-based predictive performance.

HybridGNN: A Self-Supervised Graph Neural Network for Efficient Maximum Matching in Bipartite Graphs

Solving maximum matching problems in bipartite graphs is critical in fields such as computational biology and social network analysis. This study introduces HybridGNN, a novel Graph Neural Network model designed to efficiently address complex matching problems at scale. HybridGNN leverages a combination of Graph Attention Networks (GATv2), Graph SAGE (SAGEConv), and Graph Isomorphism Networks (GIN) layers to enhance computational efficiency and model performance. Through extensive ablation experiments, we identify that while the SAGEConv layer demonstrates suboptimal performance in terms of accuracy and F1-score, configurations incorporating GATv2 and GIN layers show significant improvements. Specifically, in six-layer GNN architectures, the combinations of GATv2 and GIN layers with ratios of 4:2 and 5:1 yield superior accuracy and F1-score. Therefore, we name these GNN configurations HybridGNN1 and HybridGNN2. Additionally, techniques such as mixed precision training, gradient accumulation, and Jumping Knowledge networks are integrated to further optimize performance. Evaluations on an email communication dataset reveal that HybridGNNs outperform traditional algorithms such as the Hopcroft–Karp algorithm, the Hungarian algorithm, and the Blossom/Edmonds’ algorithm, particularly for large and complex graphs. These findings highlight HybridGNN’s robust capability to solve maximum matching problems in bipartite graphs, making it a powerful tool for analyzing large-scale and intricate graph data. Furthermore, our study aligns with the goals of the Symmetry and Asymmetry Study in Graph Theory special issue by exploring the role of symmetry in bipartite graph structures. By leveraging GNNs, we address the challenges related to symmetry and asymmetry in graph properties, thereby improving the reliability and fault tolerance of complex networks.

Fault Tolerance Management Implementation from Medium-to-Large-Scale Networks

As network infrastructures grow in complexity, ensuring high availability and resilience becomes critical, especially for medium-to-large scale networks. This study focuses on the development and implementation of fault tolerance management within Software-defined networking (SDN) environments, aimed at minimizing downtime and enhancing network reliability. SDN’s centralized control and dynamic programmability provide an ideal framework for implementing efficient fault detection and recovery mechanisms. The proposed model leverages real-time monitoring, redundancy protocols, and adaptive rerouting strategies to mitigate the impact of node or link failures. Key components of the model include failover mechanisms, load balancing, and traffic rerouting algorithms, designed to maintain seamless network operations during failures. Through simulation and testing, the model demonstrates significant improvements in network resilience, reducing recovery time and ensuring uninterrupted service delivery. This research provides a comprehensive guide to implementing fault-tolerant networks using SDN, offering scalable solutions that can be adapted to various network sizes and configurations. The findings emphasize the potential of SDN to revolutionize fault management in modern network infrastructures, making it a crucial consideration for future network design and operations.

Networking Microcontrollers and Balancing the Load on the Service Servers to Enhance the Fault Tolerance of the IoT Networks

Different types of faults occur in different layers of IoT networks, which affect their fault tolerance. The Controller and Services layers are the weakest links in an IoT network, and any failure in these layers drastically reduces its fault tolerance. The flow of transactions in these layers is also very heavy, requiring load balancing. The major challenge is to retain the maximum Fault tolerance of the IoT network in the presence of failures and varying load conditions in these Layers. This paper proposes a combination of Embedded system networking and a specialised networking of microcontrollers with Service Servers, and a Middleware within the Microcontrollers for load-balancing transactions in different communication paths. These implementations help retain the highest fault tolerance of the IoT network. The fault tolerance of an IoT is improved by 8% due to these proposed implementations.

Using DL Models in the Service Layer to Enhance the Fault Tolerance of IoT Networks

In an IoT network, the networked servers form a service layer, providing services to the users and the devices. The request to the service servers is routed through the gateway on one side of the services layer and the networked controllers on the other side. Data are transported from the sensors/devices through cluster heads en route to base stations and the controllers to the service servers, where the data are processed and sent for storage in the cloud through gateways. When any device is broken down or becomes non-operational, the inputs are not sensed, creating a gap in the data. The data transmitted from the devices would then become an incomplete flow; such data are not suitable for undertaking data analytics or predictions. The missing data must be first identified as the data flow and estimated or predicated to complete the data before they are transmitted through the cloud for storage and subsequent retrievals. This paper proposes a recurrent (RNN) neural network to predict the missing data. Two models are tested to predict the missing data: the multi-layer perceptron (MLP) model and a long short-term memory (LSTM)-based RNN model. The RNN-based model provides 99.66% accurate data prediction compared to other models.

Autonomous and ubiquitous in-node learning algorithms of active directed graphs and its storage behavior

The brain’s memory system is extraordinarily complex, evidenced by the multitude of neurons involved and the intricate electrochemical activities within them, as well as the complex interactions among neurons. Memory research spans various levels, from cellular and molecular to cognitive behavioral studies, each with its own focus, making it challenging to fully describe the memory mechanism. Many details of how biological neuronal networks encode, store, and retrieve information remain unknown. In this study, we model biological neuronal networks as active directed graphs, where each node is self-adaptive and relies on local information for decision-making. To explore how these networks implement memory mechanisms, we propose a parallel distributed information access algorithm based on the node scale of the active directed graph. Here, subgraphs are seen as the physical realization of the information stored in the active directed graph. Unlike traditional algorithms with global perspectives, our algorithm emphasizes global node collaboration in resource utilization through local perspectives. While it may not achieve the global optimum like a global-view algorithm, it offers superior robustness, concurrency, decentralization, and biological feasibility. We also tested network capacity, fault tolerance, and robustness, finding that the algorithm performs better in sparser network structures.

Enhancing Network Security in Distributed Systems Using Middle Roman Dominating Functions

A Middle Roman dominating function (MRDN) on a graph G = (V,E) is a function f:v→{0,1,2,3} satisfying the condition that every vertex u with f(u)=0 is adjacent to at most one vertex v with f(v)=2 or 3. Further if a vertex is assigned 2, then at most two of its vertices can be assigned 0 and if a vertex is assigned 3, then all its neighbours can be assigned 0. The weight of a MRDF is the value f(V(G))=∑_uϵV▒〖f(u〗). The Middle Roman domination number γ_MR (G) is the minimum weight of a MRDF on G. In this paper, we introduce Middle Roman Domination number denoted as γ_MR (G), study the properties of the function, present some characterization and determine γ_MR (G)-value for some graphs. Middle Roman Dominating Functions (MRDFs) present a unique approach within graph theory, with significant implications for various fields in computer science. By assigning values to vertices under specific constraints, MRDFs enable the optimization of resources, enhancing network security, load balancing, and energy efficiency in distributed systems. This paper explores the application of MRDFs in scenarios such as intrusion detection, resilient network design, task scheduling, and sensor activation. By minimizing the overall weight while maintaining functional requirements, MRDFs provide an effective strategy for addressing challenges in network topology, resource allocation, and fault tolerance. The versatility of MRDFs makes them a valuable tool in the development of robust and efficient computing systems.

Connectivity and diagnosability of the complete Josephus cube networks under h-extra fault-tolerant model

The h-extra connectivity and the h-extra diagnosability are key parameters for evaluating the reliability and fault-tolerance of the interconnection networks of the multiprocessor systems, and play an important role in designing and maintaining interconnection networks. Recently, various self-diagnostic models have emerged to assess the fault-tolerance in interconnection networks. These interconnection networks are typically expressed by a connected graph G(V,E). For a non-complete graph G and h≥0, the h-extra cut signifies a vertex subset R of G, whose removal results in G−R disconnected, with each remaining component containing at least h+1 vertices. And the h-extra connectivity of G is defined as the minimum cardinality of all h-extra cuts of G. The h-extra diagnosability for a graph G denotes the maximum number of detectable faulty vertices when focusing on these h-extra faulty sets only. The complete Josephus cube CJCn, a variant of Qn, exhibits superior properties compared to hypercube Qn, and also boasts higher connectivity. In this study, with the help of the exact value of the h-extra connectivity of CJCn, the explicit expression of h-extra diagnosability of CJCn under both the PMC model for n≥5 and 1≤h≤⌊n−32⌋ and the MM* model for n≥5 and 2≤h≤⌊n−32⌋ are identified to share the same value (h+1)n−(h−12)+1.

Algorithm for constructing routing to ensure fault tolerance of the communication network

Algorithm for constructing routing to ensure fault tolerance of the communication network

Structure connectivity and substructure connectivity of Möbius cubes

Abstract The connectivity is an important measurement for the fault-tolerance of networks. To provide more accurate measures for the fault-tolerance of networks than the connectivity, some generalizations of connectivity have been introduced. Substructure connectivity and structure connectivity are two extended concepts of classical connectivity. As a variant of the popular network hypercube, the Möbius cubes is also a famous interconnection network in parallel and distributed systems. In this article, we calculate $H$-substructure connectivity and $H$-structure connectivity of Möbius cubes when $H$ is isomorphic to $P_{m},C_{m}$ and $K_{1,m}$.

Examination of AI Enhanced Distributed Systems and its Effects on Software Engineering

Distributed systems are groups of independent computers that appear to the system's users as a single coherent system. These systems involve several critical factors, including network communication, concurrency, and fault tolerance, which are vital in software engineering. For example, cloud computing platforms like Amazon Web Services (AWS) use distributed systems to offer scalable, on-demand resources to millions of users worldwide. The introduction of Artificial Intelligence (AI) into software engineering marks a transformative period that reshapes traditional development processes and breaks down the complexity of distributed systems. AI automates routine tasks and simplifies complex processes, serving as a digital collaborator that enables developers to focus on strategic thinking and creativity. One significant advantage of using AI in distributed systems within software engineering is enhanced resource optimization. AI can identify irregularities that might indicate hardware malfunctions and take preventative measures to address them, such as rerouting traffic to healthier servers. However, distributed systems also have challenges, including increased complexity in system design, difficulty ensuring data consistency, and potential security vulnerabilities. The intricate structure of these systems can result in problems with high startup costs, safety risks, and the accuracy of the data provided. Integrating AI into distributed systems offers both significant advantages and disadvantages. This study evaluates how AI impacts the efficiency and security of distributed systems in software engineering. By analyzing the advantages and disadvantages of AI-enhanced distributed systems, we can gain a comprehensive understanding of their overall effectiveness and implications in the field.

High fault-tolerant performance of the divide-and-swap cube network

Two crucial metrics used to evaluate the fault tolerance of interconnection networks are connectivity and diagnosability. By improving the connectivity and diagnosability of the interconnection network, its fault tolerance can be enhanced. In this paper, we focus on determining the g-extra connectivity (0≤g≤10) of the divide-and-swap cube DSCn, as well as its diagnosability based on the pessimistic diagnosis strategy and g-extra precise diagnosis strategy, under the PMC and MM* models. The research analysis suggests that compared with some other connectivity and diagnosability of DSCn, such as classical connectivity, structure connectivity, super connectivity, and classical diagnosability, the extra connectivity/diagnosability and pessimistic diagnosability of DSCn enable it to have a higher fault tolerance. Moreover, we propose two O(Nlog2⁡N) effective diagnosis algorithms of DSCn: the g-extra diagnosis algorithm (EX-DiagnosisDSCn) and the pessimistic diagnosis algorithm (PE-DiagnosisDSCn), where the EX-DiagnosisDSCn algorithm can accurately diagnose the state of all processors in DSCn.

CLARA: A cluster-based node correlation for sampling rate adaptation and fault tolerance in sensor networks

Recently, wireless sensor networks (WSNs) have been proven as an efficient and low-cost solution for monitoring various kind of applications. However, the massive amount of data collected and transmitted by the sensor nodes, which are mostly redundant, will quickly consume their limited battery power, which is sometimes difficult to replace or recharge. Although the huge efforts made by researchers to solve such problem, most of the proposed techniques suffer from their accuracy and their complexity, which is not suitable for limited-resources sensors. Therefore, designing new data reduction techniques to reduce the raw data collected in such networks is becoming essential to increase their lifetime. In this paper, we propose a CLuster-based node correlation for sAmpling Rate adaptation and fAult tolerance, abbreviated CLARA, mechanism dedicated to periodic sensor network applications. Mainly, CLARA works on two stages: node correlation and fault tolerance. The first stage introduces a data clustering method that aims to search the correlation among neighboring nodes. Then, it accordingly adapts their sensing frequencies in a way to reduce the amount of data collected in such networks while preserving the information integrity at the sink. In the second stage, a fault tolerance model is proposed that allows the sink to regenerate the raw sensor data based on two methods: moving average (MA) and exponential smoothing (ES). We demonstrated the efficiency of our technique through both simulations and experiments. The best obtained results show that the first stage can reduce the sensor sampling rate, and accordingly the sensor energy, up to 64% while the second stage can accurately regenerate the raw data with an error loss less than 0.15.

Generalized [formula omitted]-sparse algorithms for constructing fault tolerant RBF networks

In the construction process of radial basis function (RBF) networks, two common crucial issues arise: the selection of RBF centers and the effective utilization of the given source without encountering the overfitting problem. Another important issue is the fault tolerant capability. That is, when noise or faults exist in a trained network, it is crucial that the network’s performance does not undergo significant deterioration or decrease. However, without employing a fault tolerant procedure, a trained RBF network may exhibit significantly poor performance. Unfortunately, most existing algorithms are unable to simultaneously address all of the aforementioned issues. This paper proposes fault tolerant training algorithms that can simultaneously select RBF nodes and train RBF output weights. Additionally, our algorithms can directly control the number of RBF nodes in an explicit manner, eliminating the need for a time-consuming procedure to tune the regularization parameter and achieve the target RBF network size. Based on simulation results, our algorithms demonstrate improved test set performance when more RBF nodes are used, effectively utilizing the given source without encountering the overfitting problem. This paper first defines a fault tolerant objective function, which includes a term to suppress the effects of weight faults and weight noise. This term also prevents the issue of overfitting, resulting in better test set performance when more RBF nodes are utilized. With the defined objective function, the training process is designed to solve a generalized M-sparse problem by incorporating an ℓ0-norm constraint. The ℓ0-norm constraint allows us to directly and explicitly control the number of RBF nodes. To address the generalized M-sparse problem, we introduce the noise-resistant iterative hard thresholding (NR-IHT) algorithm. The convergence properties of the NR-IHT algorithm are subsequently discussed theoretically. To further enhance performance, we incorporate the momentum concept into the NR-IHT algorithm, referring to the modified version as “NR-IHT-Mom”. Simulation results show that both the NR-IHT algorithm and the NR-IHT-Mom algorithm outperform several state-of-the-art comparison algorithms.

Encoded-Fusion-Based Quantum Computation for High Thresholds with Linear Optics.

We propose a fault-tolerant quantum computation scheme in a measurement-based manner with finite-sized entangled resource states and encoded-fusion scheme with linear optics. The encoded fusion is an entangled measurement devised to enhance the fusion success probability in the presence of losses and errors based on a quantum error-correcting code. We apply an encoded-fusion scheme, which can be performed with linear optics and active feedforwards to implement the generalized Shor code, to construct a fault-tolerant network configuration in a three-dimensional Raussendorf-Harrington-Goyal lattice based on the surface code. Numerical simulations show that our scheme allows us to achieve up to 10 times higher loss thresholds than nonencoded fusion approaches with limited numbers of photons used in fusion. Our scheme paves an efficient route toward fault-tolerant quantum computing with finite-sized entangled resource states and linear optics.

Optimizing [formula omitted]-coverage in energy-saving wireless sensor networks based on the Elite Global Growth Optimizer

For energy-constrained wireless sensor networks, enhancing network fault tolerance and extending lifetime are of paramount importance. In this study, we focus on addressing the Minimum Power k-Coverage (MinPKC) problem. The objective of MinPKC is to minimize and balance the transmission (Tx) power by sensor nodes (SNs), thus extending network lifetime. Furthermore, MinPKC requires satisfying the constraints of k-coverage for the targets to enhance network fault tolerance. The problem is non-convex, multimodal, and NP-hard. To address this problem, we propose a novel metaheuristic algorithm named Elite Global Growth Optimizer (EGGO), which incorporates efficient global search and elite evolution strategies into the GO and utilizes time-varying multi-strategies for population updates. This study extensively compares EGGO with ten popular algorithms on 20 classic benchmark test functions using the Friedman and Wilcoxon rank-sum tests. The results indicate that EGGO significantly outperforms all the compared algorithms. Ablative experiments confirm the crucial role of the proposed mechanisms in EGGO for improving algorithm performance. Meanwhile, the study implements ten MinPKC methods based on comparative algorithms and compares them with the EGGO-based MinPKC method in terms of total Tx power, network lifetime, and simulation time. The experimental results indicate that the EGGO-based MinPKC method significantly increases the network lifetime by approximately 14.2%, 38.2%, and 1.9% compared to the second-best algorithm, and by 57%, 451%, and 84.8% compared to the GO, while balancing the Tx power among SNs and reducing the total Tx power by approximately 28%, 12.7%, and 0.5% compared to the second-best algorithm, and by 47.1%, 72%, and 30% compared to the GO, respectively, when k=1,2,3. Additionally, a detailed analysis is conducted on the impact of the number of SNs, the maximum target coverage capacity of each SN, as well as the effects of obstacles and their distribution on signal strength attenuation in reducing Tx power. The source code is available at https://github.com/iNet-WZU/EGGO.

Building landscape ecological network with multi-scenario connectivity based on network fault tolerance index and networking technology in graph theory

Existing methods for constructing Landscape Ecological Networks (LEN) either focus on functional attributes or structural attributes and also do not address the dynamic impact of urban development on ecological spaces. To address these limitations, this paper proposed evaluating the maximum connectivity (k) of potential LEN, composed of existing ecological spaces, using a network fault tolerance index. We then used graph-based networking technology to construct the optimal LEN structure based on this index. Specifically speaking, first, we identified the existing LEN with the highest ecosystem service capacity and lowest ecological cost in the study area. Using four landscape pattern metrics, we comprehensively evaluated the fault tolerance index as the maximum connectivity k of potential LEN and determined that k = 7. We then modeled the existing LEN as a weighted graph and transformed the network optimization problem into a k-edge addition problem. This calculation yielded seven LEN schemes, each corresponding to different priority orders of new ecological corridors based on k value. This index captures changes in ecological space patterns and offers diverse LEN optimization solutions. It provides practitioners with flexible spatial strategies to address the dynamic impacts of urbanization.

The 4-Set Tree Connectivity of Folded Hypercube

The [Formula: see text]-set tree connectivity, as a natural extension of classical connectivity, is a very important index to evaluate the fault-tolerance of interconnection networks. Let [Formula: see text] be a connected graph and a subset [Formula: see text], an [Formula: see text]-tree of graph [Formula: see text] is a tree [Formula: see text] that contains all the vertices of [Formula: see text] and [Formula: see text]. Two [Formula: see text]-trees [Formula: see text] and [Formula: see text] are internally disjoint if and only if [Formula: see text] and [Formula: see text]. The cardinality of maximum internally disjoint [Formula: see text]-trees is defined as [Formula: see text], and the [Formula: see text]-set tree connectivity is defined by [Formula: see text]. In this paper, we show that the [Formula: see text]-set tree connectivity of folded hypercube when [Formula: see text], that is, [Formula: see text], where [Formula: see text] is folded hypercube for [Formula: see text].

Cluster connectivity and super cluster connectivity of half hypercube networks

Connectivity stands as a pivotal metric for evaluating the fault tolerance of interconnection networks. It measures the network's ability to maintain communication and operational continuity even in the face of failures. However, the traditional connectivity can not effectively reflect the fault tolerance ability of the network when failures occur in a clustered or block-like manner in the actual environment. To address this limitation, cluster connectivity and super cluster connectivity were proposed. In this paper, we explore the H (H⁎)-cluster connectivity and super H (H⁎)-cluster connectivity of the half hypercube network which is a hypercube-based compound network, where H∈{K1,r|0≤r≤⌈n/2⌉−4}.