Abstract

     With the rapid development of the Internet of Things (IoT), there are several challenges pertaining to security in IoT applications. Compared with the characteristics of the traditional Internet, the IoT has many problems, such as large assets, complex and diverse structures, and lack of computing resources. Traditional network intrusion detection systems cannot meet the security needs of IoT applications. In view of this situation, this study applies cloud computing and machine learning to the intrusion detection system of IoT to improve detection performance. Usually, traditional intrusion detection algorithms require considerable time for training, and these intrusion detection algorithms are not suitable for cloud computing due to the limited computing power and storage capacity of cloud nodes; therefore, it is necessary to study intrusion detection algorithms with low weights, short training time, and high detection accuracy for deployment and application on cloud nodes. An appropriate classification algorithm is a primary factor for deploying cloud computing intrusion prevention systems and a prerequisite for the system to respond to intrusion and reduce intrusion threats. This paper discusses the problems related to IoT intrusion prevention in cloud computing environments. Based on the analysis of cloud computing security threats, this study extensively explores IoT intrusion detection, cloud node monitoring, and intrusion response in cloud computing environments by using cloud computing, an improved extreme learning machine, and other methods. We use the Multi-Feature Extraction Extreme Learning Machine (MFE-ELM) algorithm for cloud computing, which adds a multi-feature extraction process to cloud servers, and use the deployed MFE-ELM algorithm on cloud nodes to detect and discover network intrusions to cloud nodes. In our simulation experiments, a classical dataset for intrusion detection is selected as a test, and test steps such as data preprocessing, feature engineering, model training, and result analysis are performed. The experimental results show that the proposed algorithm can effectively detect and identify most network data packets with good model performance and achieve efficient intrusion detection for heterogeneous data of the IoT from cloud nodes. Furthermore, it can enable the cloud server to discover nodes with serious security threats in the cloud cluster in real time, so that further security protection measures can be taken to obtain the optimal intrusion response strategy for the cloud cluster.

Introduction

     With the extension and expansion of Internet technology, the Internet of Things (IoT), as an important information technology, promotes the intelligent development of modern society. Intelligent IoT applications are being gradually popularized in daily life and industrial development, such as intelligent logistics, transportation, security, medical treatment, homes, and agriculture. The centralized processing mode of cloud computing is to upload all pending transactions to the cloud for execution, and the cloud uses computing resources, storage capacity, and transmission bandwidth to process all service requests sent by end users. The IoT refers to connecting any object with the network through information sensing equipment and according to the agreed protocol. Objects exchange and communicate information through information media to realize the functions of intelligent identification, positioning, tracking, supervision, and so on. The number of global IoT device connections has increased annually, and according to forecasts, the growth rate will gradually stabilize at 15%. Furthermore, data transmission, processing, and storage will add more load to cloud services. Mobile and sensor devices connected to the edge of the Internet are constantly generating new data with diverse data types [1], which will lead to great challenges in the computing resources and transmission bandwidth of traditional network architecture. At the same time, for IoT applications that require low network latency, such as automatic driving, if the traditional calculation is used as the operation model, low latency cannot be achieved, and thus the vehicle cannot make real-time decisions to avoid risk in the case of emergency braking. The tasks to be processed by the terminal equipment require strong real-time performance, i.e., the tasks must complete data transmission, analysis, and processing with minimum delay, which conflicts with the processing method of the traditional computing model. In summary, in this highly information-based era, the IoT faces multiple severe challenges: a large amount of data redundancy, cloud processing capacity bottlenecks, network bandwidth limits, data security and privacy, increased cloud power load, and increased task processing delays [2]. Intrusion detection technology is an active security protection technology. According to the different methods of data analysis, IoT intrusion detection systems can be divided into anomaly intrusion detection and misuse intrusion detection. Anomaly intrusion detection is an attack or malicious behavior that occurs when the host data in the network or the entire network does not conform to normal data specifications. Misuse intrusion detection refers to modeling certain specific attack models, determining the characteristic behavior of the attack, and matching it with the current behavior. A successful match represents malicious behavior [3]. The above problems are caused by limitations in the development of the IoT data processing mode and the increasing requirements for service quality for processing operations. The cloud collaborative network architecture has brought the terminal service quality to a new development stage and promoted fast-paced technology development. The optimization of task scheduling and application module mapping is a key problem in cloud computing, which plays an important role in the performance and power optimization of network architecture. Therefore, designing an efficient scheme and algorithm for IoT intrusion detection, task scheduling, and application module mapping is the key to improving the overall performance of the IoT architecture, which is of great research significance.

Conclusion and future work

     The IoT is a complex, dynamic environment, which poses new challenges to the deployment and algorithm performance of IoT intrusion detection. Based on the research of cloud-based IoT defense architecture, this study focused on cloud computing intrusion detection algorithms and measurement models. Considering the resource constraints of cloud nodes and the high complexity of the network environment, a measurement model of IoT intrusion detection in a cloud computing environment is proposed, and an MFE-ELM algorithm of a limit learning machine with multi-feature extraction is proposed. Experimental simulations verified the training time and detection accuracy of the proposed algorithm. In the experiment, the MFE-ELM algorithm showed good performance in cloud computing, especially in terms of accuracy and time efficiency. Through several experiments, it was proved that the MFE-ELM is an intrusion detection algorithm suitable for cloud computing environments.

Abstract

     Vehicular Ad Hoc Networks (VANET) is an emerging technology that enables a comfortable, safe, and efficient travel experience by providing mechanisms to execute applications related to traffic congestions, road accidents, autonomous driving, and entertainment. The mobile vehicles in VANET are characterized by low computational and storage capabilities. In such scenarios, to meet applications’ performance requirements, requests from vehicles are offloaded to edge and cloud servers. The high energy consumption of these servers increases operating costs and threatens the environment. Energy-aware offloading strategies have been introduced to tackle this problem. Existing works on computation offloading focus on optimizing the energy consumption of either the IoT devices/mobile/vehicles and/or the edge servers. This paper proposes a novel offloading algorithm that optimizes the energy of edge–cloud integrated computing platforms based on Evolutionary Genetic Algorithm (EGA) while maintaining applications’ Service Level Agreement (SLA). The proposed algorithm employs an adaptive penalty function to incorporate the optimization constraints within EGA. Comparative analysis and numerical experiments are carried out between the proposed algorithm, random and genetic algorithm-based offloading, and no offloading baseline approaches.

Introduction

     Vehicular Ad Hoc Networks (VANET) [1] is an emerging technology where vehicles acting as network nodes are equipped with computational resources and connectivity such as vehicle-to-vehicle (V2V), vehicle-to-infrastructure (V2I), vehicle-to-roadside (V2R), vehicle-to-sensors (V2S), vehicle-to-pedestrian (V2P), and vehicle-to-everything (V2X) communications. It enables a comfortable, safer, convenient, and efficient travel experience for users by using applications such as sending alerts for congestions and accidents, autonomous driving, video-enabled real-time navigation, interactive gaming, and entertainment [2], [3], [4]. These applications often require high computation and storage resources, and low latency to process complex operations. However, mobile vehicles have limited onboard computing and storage capabilities to process resource-intensive applications while maintaining the Quality of Services (QoS). To address this issue, a cloud-based vehicular network has been introduced. Cloud computing [5], [6] provides on-demand computational and storage resources to mobile vehicles over the Internet. The remote cloud servers have high computation capabilities that would satisfy applications processing times. However, a high latency between the vehicle and cloud resources hinders the deployment of time-critical applications such as autonomous driving. In addition, a delayed response for applications such as traffic congestion and interactive gaming becomes less reliable. To overcome vehicles-to-cloud latency issues, Vehicular Edge Computing (VEC) [7] has been introduced.

Conclusions and future work

     Computation offloading is important in edge–cloud integrated vehicular networks to execute computationally intensive applications having strict SLA requirements. However, the energy consumption of the edge–cloud integrated computing platform should be considered energy-efficiency is crucial. In this paper, an Energy-SLA-Aware evolutionary genetic algorithm is proposed for edge–cloud computation offloading in a vehicular network that executes a vehicle’s request either on the edge server to which the request is submitted or offloads the request to one of the cloud servers. The offloading decision is made in a way that the total energy consumption of a set of requests is minimized and the SLA requirements of each request are maintained in terms of latency and processing time. The SLA constraints in the proposed algorithm are handled using the adaptive penalty function. This is the first work to propose an energy-SLA-aware offloading in the vehicular network using EGA that optimizes the energy consumption of the edge and cloud servers simultaneously, while adhering to the latency and processing time constraints. Comparative analysis and numerical experiments carried out revealed that the proposed algorithm outperforms no offloading and random offloading approaches in terms of energy consumption, and no offloading, random and energy-non-SLA-aware genetic-based baseline approaches in terms of percentage of SLA violations.

Abstract

Document Sections

I. Overview of the Framework

II. Background Works

III. Proposed Framework

IV. Consensus Algorithm and Flowchart of Proposed Framework

V. Results and Discussion

VI. Conclusion

Abstract:

This manuscript describes since the resources are heterogeneous, a smart city is vulnerable to several security attacks, and to devise an effective response, it is necessary to recognize certain risks and their potential implications. The framework is responsible for the data transfer security issues in the smart city to incorporate and maintain physical, social, and industrial systems to provide high-quality secure data transmission to its residents. The proposed method of integrating the Blockchain and Internet of Things (IoT) with a consensus algorithm framework (BCIoT-CAF) to overcome the issues and secure data sharing in smart cities. The data security is enforced by splitting the blockchain network into separate networks, with any channel consisting of a limited number of approved entities, the data stored in the cloud gate server, and analysis of data achieved by IoT applications. The consensus algorithm plays an important role in retaining the blockchain’s speed, protection, and performance. Using an appropriate security algorithm, blockchain applications may greatly improve their performance. The modeling simulation of this research improves the speed, protection, and efficiency of 96% and tolerance error as 55%. The integrated evaluation results suggest that the proposed system integrates blockchain with IoT to provide a shielded communication platform in smart cities.

I Overview of the Framework

Blockchain used to share the data information securely and avoid any other fraudulent data threats[1]. IoT system implementations can be challenging and a transmitting ledger ideal for defining, authenticating, and protected data securely from IoT devices [2],[3]. Blockchain and IoT are two innovations rising in importance since they started. IoT can affect nearly ordinary things shortly. In the increased use of this tool, the risk of violence decreases [4]. To cope with this, existing techniques are not adequate. Blockchain has proven to be an innovative approach to IoT security problems and is a distributed network that relies on a consensus algorithm, ensuring agreement between distributed nodes on the status of some data [5],[6]. The central factor of the consensus algorithm that specifically defines a program operates and its output [7]. Blockchain technology attracting more coverage, revolutionize, automate the digital network of internet-based technologies [8]. This is a shared database that tracks each transaction that takes place on a network[9],[10]. It has a block spread over a node network. The consensus algorithm is a mechanism in which all the blockchain system peers decide on the existing state of the decentralized directory [11]. This ensures that consensus algorithms build stability in the blockchain network and confidence in the distributed computing system among unidentified peers [12]. The consensus protocol guarantees that a new block stored on the blockchain is the valid iteration accepted by all of the blockchain peers [13], [14].

Highlights

Abstract

Keywords

1. Introduction

2. Literature review

3. Problem formulation

4. Methodology

5. Computational experiments

6. Conclusions

CRediT authorship contribution statement

Acknowledgments

References

Abstract

The Bike Repositioning Problem (BRP) has raised many researchers’ attention in recent years to improve the service quality of Bike Sharing Systems (BSSs). It is mainly about designing the routes and loading instructions for the vehicles to transfer bikes among stations in order to achieve a desirable state. This study tackles a static green BRP that aims to minimize the CO2 emissions of the repositioning vehicle besides achieving the target inventory level at stations as much as possible within the time budget. Two types of bikes are considered, including usable and broken bikes. The Enhanced Artificial Bee Colony (EABC) algorithm is adopted to generate the vehicle route. Two methods, namely heuristic and exact methods, are proposed and incorporated into the EABC algorithm to compute the loading/unloading quantities at each stop. Computational experiments were conducted on the real-world instances having 10–300 stations. The results indicate that the proposed solution methodology that relies on the heuristic loading method can provide optimal solutions for small instances. For large-scale instances, it can produce better feasible solutions than two benchmark methodologies in the literature.

1. Introduction

In Bike Sharing Systems (BSSs), people can rent shared bikes to satisfy the needs for short-distance travel, such as the connection between home and a subway station, or just a leisure trip. However, due to the existence of asymmetric bike flows, some stations may be filled-in with returned bikes while some others are empty. For example, during the morning peak, the bike stations in residential areas might be empty, whereas those in the business area might be full. In a hilly area, the stations at the bottom can be full whereas those at the top can be empty because downhill trips are usually more than uphill trips. Therefore, the bikes need to be redistributed among all the stations after a certain period, so that a desirable inventory level can be maintained at each station to satisfy upcoming users’ demand. This operational problem is referred to as the Bike Repositioning Problem (BRP).

The repositioning operation is mainly about using a dedicated fleet of trucks or trailers to transport bikes among stations in order to reach the expected inventory level at each station (Raviv et al., 2013). There are generally two types of repositioning: static and dynamic. For the static repositioning that most of the current studies focus on (e.g., Cruz et al., 2017, Ho and Szeto, 2017, Liu et al., 2018, Szeto and Shui, 2018), the bike inventory and demand levels at each station are assumed to be relatively stable over time. The dynamic repositioning considers the variations of bike inventory and demand levels over time within a day (see Ghosh et al., 2017, Zhang et al., 2017, Shui and Szeto, 2018, Brinkmann et al., 2019). These two types of repositioning consider different application scenarios.

Highlights

Abstract

Keywords

Nomenclature

1. Introduction

2. The proposed SA-MODDE algorithm

3. Numerical experiments

4. Chemical engineering processes optimization

5. Conclusion

CRediT authorship contribution statement

Declaration of Competing Interest

Appendix A. Supplementary data

References

Abstract

This paper proposes a new multi-objective dynamic differential evolution algorithm with parameter self-adaptive strategies, named SA-MODDE. All components of the algorithm are synergically designed to reach its full potential, containing parental selection, mutation strategy, parameter setting, survival selection, constraint handling, and termination criteria. The improvement measures emphasize exploiting Pareto dominance information more efficiently. Particularly, parameter adaptation schemes are introduced based on both prior knowledges of current individual and feedback information on previous promising solutions, and their effectiveness is validated by comparison with three fixed-parameter combinations. Extensive numerical tests are conducted on multiple test suites with five state-of-the-art peer competitors. The statistical results demonstrated that the SA-MODDE exhibits good proximity and diversity in dealing with benchmark functions with various characteristics. Three industrial (bio)chemical processes, including two optimal control and one reformulated constrained tri-objective, are investigated to show the feasibility and robustness of the SA-MODDE.

1. Introduction

Engineering problems always require the simultaneous optimization of several competing objectives of interests. So far, multi-objective optimization (MOO) has been an active research field in process systems engineering [1,2]. Particularly, various multi-objective evolutionary algorithms (MOEAs), such as NSGAII, GDE3, and MOPSO, have been widely used to solve both academic and industrial MOO problems [3–5]. Usually, MOEAs have two main advantages: (1) As many diverse non-dominated solutions as possible can be found in a single run; (2) Various types of MOO problems can be handled without assumptions on objective functions and their mathematical characteristics [6].

The algorithm structure and search operator jointly affect the performance of MOEAs. The algorithm structure can be classified into two main categories: Pareto-based [3,7] and decompositionbased [8,9]. The former provides detailed Pareto dominance information of the population to facilitate individual comparison. The latter decomposes MOO problems into a set of scalar aggregation subproblems, each of which is optimized using the current information from neighboring subproblems. The two methods have their own advantages on different types of problems and are considered to be evenly matched [10]. In terms of search operator, differential evolution (DE) is simple to implement with only a few control parameters, i.e., scale factor (F ) and crossover rate (CR). Except for multi-objective DE (MODE) algorithms, many classic MOEAs also replaced the original evolutionary operators with DE and their performance was significantly enhanced, such as NSGAII-DE, SPEA2-DE, IBEA-DE, and MOEA/D-DE [11,12]. Through updates by dynamic population rather than generation to generation, Qing [13] presented the dynamic DE (DDE) operator, superior in efficiency, robustness, and storage requirements to the conventional DE. That is, each new individual that performs better than or similar to the corresponding old counterpart will immediately participate in the current population to provide information for subsequent evolution. This makes DDE more responsive to changes in population status. Despite of researches on multi-objective DDE (MODDE) algorithms [14,15], it is still very inadequate compared to MODE. Herein, we propose several improvement measures on the MODDE under Pareto-based structure. For convenience, the background of MOO problems and DDE operators are given in Supplementary Materials.

1- Introduction

2- The Principle of GA

3- The GALA software system

4- Conclusions

References

Abstract

This paper presents an Intelligent Information System for education. The system was created for teaching students to use genetic algorithm in application to optimization tasks. The system allows to quickly encode a solution of the problem and pick up most suitable configuration of genetic algorithm. The paper also demonstrates a specific example of usage of educational system to solve an optimization task. The paper contains a description of the educational system and its features, a description of its capabilities of working with genetic algorithm and its graphical interface.

Introduction

The use of information technologies (IT) in various spheres of human activity, the exponential growth of information volumes and the need to respond quickly in any situations necessitate the search for adequate ways to solve new and new emerging problems [1]. One of the most effective ways is the study, application, development and further improvement of algorithms and methods of machine computing. Finding the optimal solution is one of the problems that researchers face, both in the theoretical field and in solving engineering and production problems. Optimization problems imply the need to choose from the set of possible solutions the best from the point of view of certain criteria, satisfying given conditions and limitations.

1- Introduction

2- Background

3- Design and implementation of the parallel spectral clustering in Julia

4- Results

5- Discussion

6- Conclusion

References

Abstract

Spectral clustering is widely used in data mining, machine learning and other fields. It can identify the arbitrary shape of a sample space and converge to the global optimal solution. Compared with the traditional k-means algorithm, the spectral clustering algorithm has stronger adaptability to data and better clustering results. However, the computation of the algorithm is quite expensive. In this paper, an efficient parallel spectral clustering algorithm on multi-core processors in the Julia language is proposed, and we refer to it as juPSC. The Julia language is a high-performance, open-source programming language. The juPSC is composed of three procedures: (1) calculating the affinity matrix, (2) calculating the eigenvectors, and (3) conducting k-means clustering. Procedures (1) and (3) are computed by the efficient parallel algorithm, and the COO format is used to compress the affinity matrix. Two groups of experiments are conducted to verify the accuracy and efficiency of the juPSC. Experimental results indicate that (1) the juPSC achieves speedups of approximately 14×∼ 18× on a 24-core CPU and that (2) the serial version of the juPSC is faster than the Python version of scikitlearn. Moreover, the structure and functions of the juPSC are designed considering modularity, which is convenient for combination and further optimization with other parallel computing platforms.

Introduction

In recent years, machine learning has made great progress and become the preferred method for developing practical software, such as computer vision, speech recognition, and natural language processing [37,45,50,55]. Machine learning mainly includes supervised learning and unsupervised learning. Clustering is the main content of unsupervised learning. Among many clustering algorithms, the spectral clustering algorithm has become the popular one [32,53]. Spectral clustering is a technology originating from graph theory [17,29] that uses the edge connecting them to identify the nodes in the graph and allows us to cluster non-graphic data. Unsupervised clustering analysis algorithm can explore the internal group structure of data, which has been widely used in various data analysis occasions, including computer vision analysis, statistical analysis, image processing, medical information processing, biological science, social science, and psychology [19,44,51]. The basic principle of clustering analysis is to divide the data into different clusters. Members in the same cluster have similar characteristics, and members in different clusters have different characteristics. The main types of clustering algorithms include partitioning methods, hierarchical clustering, fuzzy clustering, density-based clustering, and model-based clustering [38]. The most widely used clustering algorithms are k-means [61], DBSCAN [39], ward hierarchical clustering [47], spectral clustering [53], birch algorithm [66], etc. It has been proven that the spectral clustering algorithm is more effective than other traditional clustering algorithms in references [46,56], but in the process of spectral clustering computation, the affinity matrix between nodes needs to be constructed, and storage of the affinity matrix requires much memory. It also takes a long time to achieve the first k eigenvectors of the Laplacian matrix. Thus, the spectral clustering algorithm is difficult to apply in the large-scale data processing.

1- Introduction

2- Data mining structure in large cloud storage system

3- Optimize algorithm design for IoT data access storage

4- Optimization methods of file storage

5- Performance test of optimization algorithm of IoT data access cloud storage

6- Conclusion

References

Abstract

The existing Internet of Things(IoT) uses cloud computing data access storage algorithms, that is, the hash algorithm has defects of low data processing efficiency and low fault tolerance rate. Therefore, HDFS is introduced to optimize cloud computing data access storage algorithms. HDFS is first used to optimize the data access storage architecture according to problems of data access storage architecture in the Internet of Things, in which factors of data access storage distribution in the IoT are fully considered, and hash values are used to optimize the configuration of data access information storage locations, so that data access storage distribution strategy can be optimized. Then, the topology of the IoT is optimized, and data block size is also optimized with effect algorithm. Finally, the design of file storage is optimized. Through simulation experiments, it is proved that the optimized cloud storage method has obvious performance advantages in file read and write speed as well as memory usage. Compared with the traditional hash algorithm, optimization algorithm proposed in the paper greatly improves file upload and download efficiency, data processing efficiency and fault tolerance rate, which fully demonstrates that the proposed cloud computing data access storage optimization algorithm is more superior.

Introduction

Cloud computing is mainly based on the Internet technology and provides users with services, uses, and interactions. Generally, dynamic and proliferative and virtualized resources are provided through the Internet. Among them, ‘‘Cloud’’ is a metaphor for the Internet and the network, which is mainly an abstract representation of the Internet and infrastructure. There are many definitions for cloud computing, and most of them are accepted by the American Institute of Technology. Today, cloud computing is a payment-based model that provides convenient, available, on-demand network access, and it only required less effort to interact a bit with the vendor if access to a configurable pool of computing resources is needed. Besides, cloud computing has the large quantity of advantages, such as ultra-large scale, virtualization, high reliability, versatility, high scalability, on-demand service, low cost and so on. Moreover, cloud computing can provide storage services in addition to computing services. Due to its multiple advantages, cloud computing is widely used in many fields. Many enterprises use cloud computing to store their own data access information, which has certain privacy, but there are still potential dangers. Therefore, data access storage optimization in cloud computing has become one of the key research topics among scholars today [1–3].

This paper addresses a multi-objective feature selection problem for early time series classification. Previous research has focused on how many features to consider for a classifier, but has not considered the starting time of classification, which is also important for early classification. Motivated by this, we developed a mathematical model for which the objectives are to maximize classification performance and minimize the starting time and execution time of classification. We designed an efficient genetic algorithm to generate solutions with high probability. In experiment, we compared the proposed algorithm and general genetic algorithm under various experimental settings. From the experiment, we verified that the proposed algorithm can find a better feature set in terms of classification performance, starting time and execution time of classification than feature set found by general genetic algorithm.

Introduction

Time series classification is used to predict the class label of a time series instance by a welltrained classifier (Deng et al., 2013). That is, if a time series instance , ? ? (?) = (? , is given, its label, , is predicted by the classifier as (?) 1 , ? (?) 2 , ⋯, ? (?) ? ) ? (?) ?( ∙ ) ? (?) = ? (? . Time series classification is used to accomplish tasks in many fields, including fault (?) ) detection in the manufacturing field (Lee et al., 2017), disease diagnosis in the medical field (Lacy et al., 2018), and stock trend analysis in the financial field (Moews et al., 2019). Various classifiers such as neural networks (NNs) and support vector machines (SVMs) are employed and modified to classify time series. Ignatov (2018) employed a convolutional neural network (CNN) to recognize human activity from accelerometer data. Kim and Cho (2018) developed a C-LSTM (CNN- Long Short-Term Memory model) NN to detect anomalies in web traffic data. CNNs and LSTMs in the developed model extracted spatial features and temporal characteristics, respectively. Emoto et al. (2018) used NNs to detect low-intensity snoring episodes from a sleeping sound dataset. Cheng and Dong (2019) employed SVM technology to monitor the nanomachining process with respect to the machining performance. Kalantarian et al. (2016) used SVMs to segment streaming timeseries audio signals probabilistically.

This work is devoted to the study of application of new topologies in the design of networks-on-chip (NoCs). It is proposed to use two-dimensional optimal circulant topologies for NoC design, and it is developed an optimized routing algorithm with the decreased memory usage. The proposed routing algorithm was compared with Table routing, Clockwise routing, and Adaptive routing algorithms, previously developed for ring circulant topologies, and specialized routing algorithm for multiplicative circulants. The results of synthesis of routers implementing proposed routing algorithms are presented. The cost of ALM and register resources for the implementation of communication subsystems in NoCs with circulant topologies is estimated.

Introduction

Multiprocessor systems-on-chip (MPSoCs) [1] are currently one of the fastest growing areas in computing. An extensive increase in the size of the chip and the number of transistors per unit area allows developing chips with tens and hundreds of processor cores even now. At the same time, the problem of effective organization of a communication subsystem that would ensure quick data exchange between nodes of such NoCs is becoming urgent [2]. Since communication is carried out within the framework of a single chip, laws and principles that exist in telecommunication networks work differently in NoCs; therefore, the development of new solutions and methods for organizing data transfer in such networks is required. In particular, it is the topology that has a significant impact on NoC performance. The most common are classical regular topologies such as mesh [3] and torus [4], which do not always meet modern requirements for NoCs, especially with an increase in the number of nodes [5]. Different researchers suggest other topology options among which we can distinguish hypercube [6, 7, 8], chordal ring [9, 10], spidergon [11], L-networks [12]. Their feature is that they can be reduced to presentation in the form of ring-like graphs called circulant topologies in the general form. Optimal circulants have several significant advantages over mesh and torus topologies – better structural survivability, reliability, and connectivity [13, 14].