Set Of Nodes Research Articles

Optimizing Connectivity and Coverage for Millimeter-Wave-Based Networks

In this article, the problem of achieving the minimum backbone connectivity cost while simultaneously maximizing user coverage for 5G millimeter-wave (mmWave)-based networks is considered. Let G=(N,E) be an input graph instance with a set of nodes N (base stations) and a set of edges E. It is assumed that G represents a wireless backbone network. Let M represent a set of users to be covered by G. Note that mmWave technology has been considered in the literature as an important candidate solution for 5G networks due to its low latency. However, there remain some problems to be addressed before using this technology. A serious one is that millimeter waves cannot cover large transmission distances. In this article, the proposed methodology consists of formulating mixed-integer programming models to deal with the problem from a management point of view. Our models allow the determination of which of the nodes of G should be active and connected while simultaneously maximizing the total number of covered users. The models are solved with the CPLEX solver using its branch and cut and automatic Benders decomposition algorithms. For this purpose, symmetric complete and sparse graphs are considered. Using the symmetry concept, it is considered that the distances between base stations and users and between base stations themselves are symmetrical. Finally, an efficient local search meta-heuristic is proposed that allows for finding near-optimal solutions. Our numerical experiments indicate that the problem is hard to solve optimally. Thus, instances with up to 40 nodes and 500 users have been solved to optimality so far. In particular, it is observed that one of the models presents slightly better performance in terms of CPU time. Finally, the heuristic approach allows us to obtain tight solutions with less computational effort when dealing with even larger instances of the problem.

Identifying critical nodes of cyber–physical power systems based on improved adaptive differential evolution

The identification and protection of critical nodes have a significant influence on the reliability and robustness of the cyber–physical power system (CPPS), which can effectively reduce the risk of cascading failures. Firstly, this paper establishes a one-to-one coupled cascading fault model, which considers different topological characteristics of power and cyber networks. Based on the interdependence between the two networks, the cascading fault propagation mechanism after node failures in CPPS is analyzed. Then, a critical node identification method based on improved adaptive differential evolution (JADE) is proposed to identify the sets of critical nodes that can maximize the impact on the system load of CPPS. Combined with the cascading failure characteristics of CPPS, in the population generation strategy, the test vectors that do not meet the conditions after the crossover operation are filtered and replaced to improve the search efficiency of the algorithm. Finally, in the case study, an interdependent CPPS is constructed with an IEEE 39-bus system and a scale-free network of the same nodes. The simulation results verify the effectiveness of the proposed node importance assessment strategy. In addition, it is also shown that evaluating the critical nodes in power systems is important for enhancing the robustness and ensuring the security of the power grid operation.

Controllability of networked multiagent systems based on linearized Turing’s model

Turing’s model has been widely used to explain how simple, uniform structures can give rise to complex, patterned structures during the development of organisms. However, it is very hard to establish rigorous theoretical results for the dynamic evolution behavior of Turing’s model since it is described by nonlinear partial differential equations. We focus on controllability of Turing’s model by linearization and spatial discretization. This linearized model is a networked system whose agents are second order linear systems and these agents interact with each other by Laplacian dynamics on a graph. A control signal can be added to agents of choice. Under mild conditions on the parameters of the linearized Turing’s model, we prove the equivalence between controllability of the linearized Turing’s model and controllability of a Laplace dynamic system with agents of first order dynamics. When the graph is a grid graph or a cylinder grid graph, we then give precisely the minimal number of control nodes and a corresponding control node set such that the Laplace dynamic systems on these graphs with agents of first order dynamics are controllable.

A thermal assessment simplification exploration for the structural constraint effect on bearing temperature

Although an extensive research effort on the structural constraint role in bearing heating was done by scholars, often many researchers either neglected the sub structure effect for model simplification or considered more influencing factors to construct a complicated thermal model for higher evaluation precision. As a result, a lightweight and accurate assessment has been not available so far. Furthermore, they usually only made some basic assumptions and qualitative analyses when creating and improving the thermal predictive models to explore the heat transfer of bearings, and hence their findings usually lack sufficient theoretical supports, especially the quantitative bases. For an efficient assessment, this paper devotes to exploring how the structural constraint impact on the heat conduction of bearings, and accordingly present a more practical thermal grid to evaluate bearing heating efficiently. Firstly, the structure and installation notes of bearings were statistically analyzed. Next, a formula was constructed to implement the contrast of the heat transfer capacity between the axial and radial directions of bearing rings, and then a novel radial thermal equivalent resistance was proposed to represent the heat conduction capacity of bearing rings. We accordingly optimized the bearing node setting scheme to develop an efficient semi-empirical thermal grid for high-speed angular contact ball bearings, in which the oil-air separation and gray-box theory was also introduced to describe the heat convection in bearing cavities. Finally the improved thermal network for a motored spindle was planned to verify the above-proposed work, and the simulation results based on the current thermal models of bearings were also obtained and contrasted with the experimental values. For a further validation, the polynomial interpolation on test data, meanwhile, was performed to observe the temperature variation trend. The result of comparative analysis indicates that we show a more proper thermal assessment on bearing temperature.

Optimizing Data Processing: A Comparative Study of Big Data Platforms in Edge, Fog, and Cloud Layers

Intelligent applications in several areas increasingly rely on big data solutions to improve their efficiency, but the processing and management of big data incur high costs. Although cloud-computing-based big data management and processing offer a promising solution to provide scalable and abundant resources, the current cloud-based big data management platforms do not properly address the high latency, privacy, and bandwidth consumption challenges that arise when sending large volumes of user data to the cloud. Computing in the edge and fog layers is quickly emerging as an extension of cloud computing used to reduce latency and bandwidth consumption, resulting in some of the processing tasks being performed in edge/fog-layer devices. Although these devices are resource-constrained, recent increases in resource capacity provide the potential for collaborative big data processing. We investigated the deployment of data processing platforms based on three different computing paradigms, namely batch processing, stream processing, and function processing, by aggregating the processing power from a diverse set of nodes in the local area. Herein, we demonstrate the efficacy and viability of edge-/fog-layer big data processing across a variety of real-world applications and in comparison to the cloud-native approach in terms of performance.

Toward Stabilizable Large-Scale Boolean Networks by Controlling the Minimal Set of Nodes

This paper studies <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">structural</i> controllers and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">distributed</i> pinning controllers for the global stabilization of Boolean networks (BNs) by integrating the information on their network structures with nodal dynamics. The main contribution is that several computationally efficient procedures are presented to reduce the number of controlled nodes and to determine a minimal set of controlled nodes without using the brute-force searches. The primary objective is to identify a minimal set of nodes that need to be controlled in the structural controllers for the strong structural stabilization of BNs when network structures is available yet nodal dynamics are unknown. To this end, a theorem shows this minimum controlled node problem can be addressed by seeking the minimum feedback vertex set of network structure. The subsequent part concentrates on designing distributed pinning controllers that merely rely on the node-to-node information exchanges for the global stabilization of BNs with the full knowledge of the nodal dynamics. Several sufficient conditions are provided by utilizing the irreducibility and activation-inhibition network structures to reduce the conservatism. Notably, we claim that, for regulatory BNs without positive cycles, the minimal set of pinned nodes can be determined with a linear amount of time subject to the total number of logical operators in the nodal dynamics. Finally, the effectiveness of these results are validated by three case studies.

Power Attributed Graph Embedding and Clustering.

Representation learning is a central problem of attributed networks (ANs) data analysis in a variety of fields. Given an attributed graph, the objectives are to obtain a representation of nodes and a partition of the set of nodes. Usually, these two objectives are pursued separately via two tasks that are performed sequentially, and any benefit that may be obtained by performing them simultaneously is lost. In this brief, we propose a power-attributed graph embedding and clustering (PAGEC for short) in which the two tasks, embedding and clustering, are considered together. To jointly encode data affinity between node links and attributes, we use a new powered proximity matrix. We formulate a new matrix decomposition model to obtain node representation and node clustering simultaneously. Theoretical analysis shows the close connections between the new proximity matrix and the random walk theory on a graph. Experimental results demonstrate that the PAGEC algorithm performs better, in terms of clustering and embedding, than state-of-the-art algorithms including deep learning methods designed for similar tasks in relation to attributed network datasets with different characteristics.

A Node sets based Fast and Scalable Frequent Itemset (FSFIM) Algorithm for Mining Big Data using MapReduce Paradigm

A Node sets based Fast and Scalable Frequent Itemset (FSFIM) Algorithm for Mining Big Data using MapReduce Paradigm

Diffusion Source Inference for Large-Scale Complex Networks Based on Network Percolation.

This article studies the diffusion-source-inference (DSI) problem, whose solution plays an important role in real-world scenarios such as combating misinformation and controlling diffusions of information or disease. The main task of the DSI problem is to optimize an estimator, such that the real source can be more precisely targeted. In this article, we assume that the state of a number of nodes, called observer set, in a network could be investigated if necessary, and study what configuration of those nodes could facilitate a better solution for the DSI problem. In particular, we find that the conventional error distance metric cannot precisely evaluate the effectiveness of varied DSI approaches in heterogeneous networks, and thus propose a novel and more general measurement, the candidate set, that is formulated to contain the diffusion source for sure. We propose the percolation-based evolutionary framework (PrEF) to optimize the observer set such that the candidate set can be minimized. Hence, one could further conduct more intensive investigation or search on only a few nodes to target the source. To achieve that, we first theoretically show that the size of the candidate set is bounded by the size of the largest component cover, and demonstrate that there are some similarities between the DSI problem and the network immunization problem. We find that, given the associated direction information of the diffusion is known on observers, the minimization of the candidate set is equivalent to the minimization of the order parameter if we view the observer set as the removal node set. Hence, PrEF is developed based on the network percolation and evolutionary algorithm. The effectiveness of the proposed method is validated on both synthetic and empirical networks in regard to varied circumstances. Our results show that the developed approach could achieve much smaller candidate sets compared to the state of the art in almost all cases, e.g., it is better in 26 out of 27 empirical networks and 155 out of 162 cases regarding the critical threshold. Meanwhile, our approach is also more stable, i.e., it works well irrespective of varied infection probabilities, diffusion models, and underlying networks. More importantly, we provide a framework for the analysis of the DSI problem in large-scale networks.

A Generalized Nesterov-Accelerated Second-Order Latent Factor Model for High-Dimensional and Incomplete Data.

High-dimensional and incomplete (HDI) data are frequently encountered in big date-related applications for describing restricted observed interactions among large node sets. How to perform accurate and efficient representation learning on such HDI data is a hot yet thorny issue. A latent factor (LF) model has proven to be efficient in addressing it. However, the objective function of an LF model is nonconvex. Commonly adopted first-order methods cannot approach its second-order stationary point, thereby resulting in accuracy loss. On the other hand, traditional second-order methods are impractical for LF models since they suffer from high computational costs due to the required operations on the objective's huge Hessian matrix. In order to address this issue, this study proposes a generalized Nesterov-accelerated second-order LF (GNSLF) model that integrates twofold conceptions: 1) acquiring proper second-order step efficiently by adopting a Hessian-vector algorithm and 2) embedding the second-order step into a generalized Nesterov's acceleration (GNA) method for speeding up its linear search process. The analysis focuses on the local convergence for GNSLF's nonconvex cost function instead of the global convergence has been taken; its local convergence properties have been provided with theoretical proofs. Experimental results on six HDI data cases demonstrate that GNSLF performs better than state-of-the-art LF models in accuracy for missing data estimation with high efficiency, i.e., a second-order model can be accelerated by incorporating GNA without accuracy loss.

Math‐based reinforcement learning for the adaptive budgeted influence maximization problem

AbstractIn social networks, the influence maximization problem requires selecting an initial set of nodes to influence so that the spread of influence can reach its maximum under certain diffusion models. Usually, the problem is formulated in a two‐stage un‐budgeted fashion: The decision maker selects a given number of nodes to influence and observes the results. In the adaptive version of the problem, it is possible to select the nodes at each time step of a given time interval. This allows the decision‐maker to exploit the observation of the propagation and to make better decisions. This paper considers the adaptive budgeted influence maximization problem, that is, the adaptive problem in which the decision maker has a finite budget to influence the nodes, and each node requires a cost to be influenced. We present two solution techniques: The first is an approximated value iteration leveraging mixed integer linear problems while the second exploits new concepts from graph neural networks. Extensive numerical experiments demonstrate the effectiveness of the proposed approaches.

Mobile Adhoc Network Risk Profiles - An Overview of Existing Network Traffic Datasets to DetermineIdeal Axiom Criteria

A Mobile Adhoc networks also known as MANET or Wireless Adhoc Network is a network that usually has aroutable networking environment on top of a Link Layer ad hoc network. It consist of a set of mobile nodes connected wirelessly in a self-configured, self-healing network without having a fixed infrastructure. Recent studies and fieldwork have pointed in the direction of making MANETS a publicly viable option in the event of another world event/crisis such as the recent COVID-19 pandemic. As opposed to their traditional military and emergency uses, this has become a focal point due to the evident strain that was observed on mainstream Internet Service Providers as substantial adjustments had to be made to facilitate a new ’working-from-home’ public. A primary aspect that must be considered before public adoption is addressing the issue of MANET risk and Security which leads into identifying and classifying risks associated with MANETS.

Towards improving community detection in complex networks using influential nodes

Abstract Complex network analysis is inspired by empirical studies of real-world networks such as computer networks, technology networks and social networks. The analysis of community structure in complex networks is understood as an important issue by the research society. A community is a set of nodes in a network where the density of connections is high. The insight in the literature shows many approaches to identify influential nodes, but these approaches only lead to finding community centres. Meanwhile, clustering techniques are effectively used for community detection, where they can reveal group structure and hidden connections by considering topological and demographic information. This article presents an ensemble clustering algorithm based on influential nodes to improve community detection in complex networks. Considering different characteristics of the network, the proposed method seeks to discover common interests between users and their behaviours to identify the most suitable communities. First, a set of influential nodes are identified as community centres. Then, these centres are considered as cluster centres. After that, primary clusters are created based on the determined centres. Finally, the primary clusters are reclustered to form the final clusters. Here, the final clusters are considered as communities of users in the network. The simulation has been performed on real-world networks and the results confirm the effectiveness of the proposed method. Specifically, the communities identified by the proposed method are 2.1% better than the best existing state-of-the-art method in terms of modularity. Keywords: complex network; community detection; influential nodes; ensemble clustering.

Time-domain acoustic wave propagations in multi-fluids using a weak-form meshfree method

In this work, we focus on the derivation of the weak-form for meshfree methods in analyzing the time-domain acoustic wave propagation in multi-fluids. Due to the employment of meshfree shape functions not restricted to a local background cell, the continuity condition for acoustic particle velocity cannot be spontaneously satisfied, leading to inaccurate simulations of acoustic wave upon the interface. Thus, the penalty function method is utilized here in the weak-form for meshfree methods in order to cure this discontinuity issue without introducing any addition degrees of freedom. By conducting a number of numerical analyses, the numerical results obtained from a radial point interpolation meshfree method are in accord with the analytical solutions and the numerical results of bilinear and quadratic finite elements, validating the effectiveness of the weak-form derived for meshfree methods. Moreover, the numerical accuracy of the used meshfree method can surpass those of bilinear and quadratic finite elements when the same sets of nodes are employed, especially for relatively high frequencies.

PRUNING MINIMUM SPANNING TREES AND CUTTING LONGEST EDGES TO CONNECT A GIVEN NUMBER OF NODES BY MINIMIZING TOTAL EDGE LENGTH

Background. Whereas in many tasks of designing efficient telecommunication networks, the number of network nodes is limited, the initial choice of nodes is wider. There are more possible locations than factually active tools to be settled to those locations to further satisfy consumers. This induces an available node constraint problem.&#x0D; Objective. Given an initial set of planar nodes, the problem is to build a minimum spanning tree connecting a given number of the nodes, which is less than the cardinality of the initial set. Therefore, the available node constraint problem aims at building an optimally minimum spanning tree to connect a given number of planar nodes being less than an initial number of nodes by minimizing the tree length.&#x0D; Methods. The initial set of nodes is triangulated. This gives a set of edges, whose lengths are calculated and used as graph weights. A minimum spanning tree is built over this graph. The desired number of nodes is reached by pruning the minimum spanning tree connecting the initial number of nodes, where free edges whose weights are the largest are iteratively removed from the tree. The other approach, the cutting method, removes longest edges off the initial minimum spanning tree, regardless of whether they are free or not.&#x0D; Results. Unlike the pruning method, the method of cutting longest edges may result in a minimum spanning tree connecting fewer nodes than the desired number. However, the cutting method often outputs a shorter tree, especially when the edge length varies much. Besides, the cutting method is slower due to it iteratively rebuilds a minimum spanning tree.&#x0D; Conclusions. The problem is initially solved by the pruning method. Then the cutting method is used and its solution is compared to the solution by the pruning method. The best tree is shorter. A tradeoff for the nodes and tree length is possible.

Optimal layout scheme design of distribution network micro PMU based on information entropy theory

Abstract This paper proposes a design method of distribution network micro PMU optimal layout scheme based on information entropy theory, realizes the optimal configuration of distribution network micro PMU, accurately reflects the operation status of distribution network, and ensures the smooth operation of power system. On the premise that the number of PMUs is the least and the distribution network is completely observable, the dynamic characteristics of uncertain nodes such as distributed generation in the distribution network and the existing traditional measurement equipment and measurement information are comprehensively considered, and the information entropy theory is used to measure and evaluate the uncertainty of the distribution network. The distribution network micro PMU distribution point set taking into account the network uncertainty is selected based on the information entropy evaluation method. In the round by round iterative solution, greedy algorithm is used to select the node with the lowest distribution network uncertainty from the existing network nodes in each round as the installation node of the distribution network micro PMU, and obtain the installation node set of the micro PMU, so as to complete the design of the distribution network micro PMU optimal layout scheme. The experiment shows that the optimal distribution network micro PMU layout scheme designed by this method can effectively realize the optimal configuration of PMU, and can realize the full observability of the distribution network with a small number of PMU configurations.

Topological approach and analysis of clustering in consensus networks

We study clustering properties of networks of single-integrator nodes over a directed graph, in which the nodes converge to steady-state values. These values define clustering groups of nodes, which are considered dependent on interaction topology and edge weights. Focusing on the interaction topology of the network, in this paper, we introduce the notion of topological clusters, which are sets of nodes that converge to an identical value due to the topological characteristics of the network, independent of the value of the edge weights. We then investigate properties of topological clusters and present a necessary and sufficient condition for a set of nodes to form a topological cluster. We also provide an algorithm for finding topological clusters, which is validated by an example.

Majority vote in social networks

Consider a graph G and suppose that initially each node is colored either black or white. In the majority model, in each round all nodes simultaneously update their color to the most frequent color among their neighbors.Experiments on the graph data from the real world social networks (SNs) suggest that if an extremely small set of high-degree nodes, often referred to as the elites, all agree on a color, that color becomes the dominant color at the end of the process. We propose two countermeasures that can be adopted by individual nodes relatively easily and guarantee that the elites will not have this disproportionate power to engineer the dominant output color. The first countermeasure essentially requires each node to make some new connections at random, while the second one demands the nodes to be more reluctant towards changing their color. We verify their effectiveness and correctness both theoretically and experimentally.We also investigate the majority model and a variant of it when the initial coloring is random on the real world SNs and several random graph models. In particular, our results on the Erdős-Rényi and regular random graphs confirm or support several theoretical findings or conjectures by the prior work regarding the threshold behavior of the process.

A Resource Allocation Model for Mixed-Grid Optical Networks

Due to cost and service level agreement, upgrading network infrastructure is always challenging for network operators, particularly for backbone optical networks (ONs). Nowadays, to support several bandwidth-hungry applications, network operators adopt the migration process from fixed-grid nodes to flex-grid in backbone ONs. However, without proper planning, it may lead to inefficient resource utilization. This paper proposes optimization models for resource allocation in mixed-grid ONs, which initially identifies the set of eligible nodes for upgradation from fixed-grid to flex-grid capabilities for a given set of offline traffic and then uses them in the network to maximize the resource utilization. We formulate an integer linear programming (ILP) problem, named Opti-node, to determine the set of nodes selected for fixed-grid to flex-grid conversion in mixed-grid ONs. We then introduce an ILP, named Opti-resource, to enhance the resource utilization based on the determined set of nodes converted from fixed-grid to flex-grid using Opti-node. We prove that the decision problem of resource allocation in mixed-grid ONs is NP-Complete. Heuristic approaches based on the ILP-based approach and simulated annealing are introduced for a large problem size when Opti-resource is not tractable. We evaluate the proposed resource allocation model extensively, considering different networks, and observe that the simulated annealing-based approach performs better in terms of blocking ratio and spectrum utilization than the ILP-based heuristic approach, but it requires additional computation time.

The application of heterogeneous graph neural network and deep reinforcement learning in hybrid flow shop scheduling problem

The hybrid flow shop scheduling problem (HFSP) is a fundamental optimization problem in the process industries. HFSP needs to consider both job selection and machine allocation. The existing HFSP solution methods represented by deep reinforcement learning (DRL) are challenging to extract complex state features and lack certain adaptability in dealing with large-scale HFSP. To solve HFSP with a large scale and relatively strong flexibility, we propose an end-to-end DRL architecture based on the heterogeneous graph neural network to learn an optimal scheduling policy. First of all, by adding a set of machine nodes, the disjunctive graph of the traditional flexible scheduling problem is extended and transformed into a heterogeneous graph, which intuitively represents the allocation relationship between operations and machines, and it is regarded as the scheduling state at different times; secondly, a new HFSP heterogeneous graph neural network (HGNN) algorithm is established to embed potential relationships between different types of nodes and edges, and an embedding of the entire graph is generated; finally, we use the graph-level representation vectors of heterogeneous graphs as input to the proximal policy optimization (PPO) algorithm for learning the optimal scheduling policy. The experimental results show that compared with several well-known heuristic algorithms, the scheduling policy obtained by the architecture through learning can have good generalization performance in simple and complex problems, respectively, and has a relatively high solution efficiency.