Cardinality Of Nodes Research Articles

Node cardinality estimation in a heterogeneous wireless network deployed over a large region using a mobile base station

We consider the problem of estimation of the node cardinality of each node type in a heterogeneous wireless network with T types of nodes deployed over a large region, where T≥2 is an integer. A mobile base station (MBS), such as that mounted on an unmanned aerial vehicle, is used in such cases since a single static base station is not sufficient to cover such a large region. The MBS moves around in the region and makes multiple stops, and at the last stop, it is able to estimate the node cardinalities for the entire region. In this paper, two schemes, viz., HSRC-M1 and HSRC-M2, are proposed to rapidly estimate the number of nodes of each type. Both schemes have two phases, and they are performed at each stop. We prove that the node cardinality estimates computed using our proposed schemes are equal to, and hence as accurate as, the estimates that would have been obtained if a well-known estimation protocol designed for homogeneous networks in prior work were separately executed T times. Closed-form expressions for the expected number of slots required by HSRC-M1 to execute and the expected energy consumption of a node under HSRC-M1 are computed. The problem of finding the optimal tour of the MBS around the region, which covers all the nodes and minimizes the travel cost of the MBS, is formulated and shown to be NP-complete, and a greedy algorithm is provided to solve it. Using simulations, it is shown that the numbers of slots required by the proposed schemes, HSRC-M1 and HSRC-M2, for computing node cardinality estimates are significantly less than the number of slots required for T separate executions of the above estimation protocol for homogeneous networks.

Fair graph representation learning: Empowering NIFTY via Biased Edge Dropout and Fair Attribute Preprocessing

The increasing complexity and amount of data available in modern applications strongly demand Trustworthy Learning algorithms that can be fed directly with complex and large graphs data. In fact, on one hand, machine learning models must meet high technical standards (e.g., high accuracy with limited computational requirements), but, at the same time, they must be sure not to discriminate against subgroups of the population (e.g., based on gender or ethnicity). Graph Neural Networks (GNNs) are currently the most effective solution to meet the technical requirements, even if it has been demonstrated that they inherit and amplify the biases contained in the data as a reflection of societal inequities. In fact, when dealing with graph data, these biases can be hidden not only in the node attributes but also in the connections between entities. Several Fair GNNs have been proposed in the literature, with uNIfying Fairness and stabiliTY (NIFTY) (Agarwal et al., 2021) being one of the most effective. In this paper, we will empower NIFTY’s fairness with two new strategies. The first one is a Biased Edge Dropout, namely, we drop graph edges to balance homophilous and heterophilous sensitive connections, mitigating the bias induced by subgroup node cardinality. The second one is Attributes Preprocessing, which is the process of learning a fair transformation of the original node attributes. The effectiveness of our proposal will be tested on a series of datasets with increasingly challenging scenarios. These scenarios will deal with different levels of knowledge about the entire graph, i.e., how many portions of the graph are known and which sub-portion is labelled at the training and forward phases.

Techniques for accelerating branch-and-bound algorithms dedicated to sparse optimization

Sparse optimization–fitting data with a low-cardinality linear model–is addressed through the minimization of a cardinality-penalized least-squares function, for which dedicated branch-and-bound algorithms clearly outperform generic mixed-integer-programming solvers. Three acceleration techniques are proposed for such algorithms. Convex relaxation problems at each node are addressed with dual approaches, which can early prune suboptimal nodes. Screening methods are implemented, which fix variables to their optimal value during the node evaluation, reducing the subproblem size. Numerical experiments show that the efficiency of such techniques depends on the node cardinality and on the structure of the problem matrix. Last, different exploration strategies are proposed to schedule the nodes. Best-first search is shown to outperform the standard depth-first search used in the related literature. A new strategy is proposed which first explores the nodes with the lowest least-squares value, which is shown to be the best at finding the optimal solution–without proving its optimality. A C++ solver with compiling and usage instructions is made available.

CoRMAC: A Connected Random Topology Formation With Maximal Area Coverage in Wireless Ad-Hoc Networks

R1C2Random geometric graphs can be used in constructing topology formations for wireless ad-hoc networks (WANETs), including wireless sensor networks, flying ad-hoc networks, and others. They are useful for energy-saving schemes where a randomly alternating subset of deployed nodes is turned off temporarily (without compromising the network connectivity). This also improves network security by periodically re-routing the data flow, which makes it harder for third parties to run a traffic analysis. In the area and target coverage scenarios, a WANET deployment is desired to have maximal area coverage efficiency, which implies covering the largest possible area using the fewest number of nodes by maintaining the connectivity as well. Although deterministic topology formations offering optimal area coverage are known, a random node deployment method that grants connectivity and area coverage maximality has not been presented, to the best of our knowledge. This study introduces a novel topology formation method, called CoRMAC, that consistently yields tree-formed random geometric graphs that are guaranteed to be connected and offer maximal area coverage for any given area size and node cardinality. The area coverage maximality of CoRMAC is formally proven. Extensive theoretical and computational analyses have been provided to demonstrate its graph-theoretic, Euclidean, and networking features. Moreover, comparisons were made with other approaches to show the effectiveness of the proposed method.

Optimizing target nodes selection for the control energy of directed complex networks

The energy needed in controlling a complex network is a problem of practical importance. Recent works have focused on the reduction of control energy either via strategic placement of driver nodes, or by decreasing the cardinality of nodes to be controlled. However, optimizing control energy with respect to target nodes selection has yet been considered. In this work, we propose an iterative method based on Stiefel manifold optimization of selectable target node matrix to reduce control energy. We derive the matrix derivative gradient needed for the search algorithm in a general way, and search for target nodes which result in reduced control energy, assuming that driver nodes placement is fixed. Our findings reveal that the control energy is optimal when the path distances from driver nodes to target nodes are minimized. We corroborate our algorithm with extensive simulations on elementary network topologies, random and scale-free networks, as well as various real networks. The simulation results show that the control energy found using our algorithm outperforms heuristic selection strategies for choosing target nodes by a few orders of magnitude. Our work may be applicable to opinion networks, where one is interested in identifying the optimal group of individuals that the driver nodes can influence.

Fast node cardinality estimation and cognitive MAC protocol design for heterogeneous machine-to-machine networks

Machine-to-Machine (M2M) networks are an emerging technology with applications in numerous areas including smart grids, smart cities, vehicular telematics, and healthcare. In this paper, we design two estimation protocols for rapidly obtaining separate estimates of the number of active nodes of each traffic type in a heterogeneous M2M network with $T$ types of M2M nodes (e.g., those that send emergency, periodic, normal type data etc), where $T \geq 2$ is an arbitrary integer. One of these protocols, Method I, is a simple scheme, and the other, Method II, is more sophisticated and performs better than Method I. Also, we design a medium access control (MAC) protocol that supports multi-channel operation for a heterogeneous M2M network with an arbitrary number of types of M2M nodes, operating as a secondary network using Cognitive Radio technology. Our Cognitive MAC protocol uses the proposed node cardinality estimation protocols to rapidly estimate the number of active nodes of each type in every time frame; these estimates are used to find the optimal contention probabilities to be used in the MAC protocol. We compute a closed form expression for the expected number of time slots required by Method I to execute as well as a simple upper bound on it. Also, we mathematically analyze the performance of the Cognitive MAC protocol and obtain expressions for the expected number of successful contentions per frame and the expected amount of energy consumed. Finally, we evaluate the performances of our proposed estimation protocols and Cognitive MAC protocol using simulations.

Mitigating the effect of multipath using cross-correlation: application to underwater network cardinality estimation

Number of node cardinality is an important parameter for a networks proper operation and this parameter can be determined using conventional protocol-based techniques, but these techniques have several limitations in underwater environment due to large propagation latency, high error rate, node mobility, non-negligible capture effect and high path loss. To develop a suitable cardinality estimation technique in presence of unique characteristics of underwater network, a statistical signal processing approach based on cross-correlation of Gaussian signals received at multiple sensors has been proposed in our previous works. In the initial formulation of this approach, a simplified model has been investigated without considering the multipath propagation effect. One of the common challenges for underwater wireless communication is multipath propagation of signals which result in inter-symbol interference ISI. An important feature of cross-correlation is its ability to mitigate the multipath effect which is demonstrated in this paper and applied to our previously proposed estimation scheme for multipath compensation. It is shown that, due to high dispersion coefficient of the medium, multipath effects on estimation results are negligible and a generalised process of multipath compensation for any dispersion factor is obtained to improve the robustness of this scheme.

A novel hybrid approach for link prediction problem in social network

Link prediction in dynamic social network is an inherent challenging task to find out the intrinsic associations among the objects. This association can be discovered with the help of pattern of connection in already linked objects. This paper addresses the three novel hybrid feature extraction methodologies that leverage the significant insight of existing model available for link prediction. The proposed technique offers better agreement of causal link to be happened between pair of objects in future. The conventional link prediction models are applying features which are typically grounded on the node cardinality. These predictor models are common neighbour predictor, Adamic/Adar, Jaccard's coefficient, preferential attachment, friends measures. So, hybrid feature extraction techniques based on principle of feature ensemble is introduced to generate predictive model to be learned for link prediction. Jacccard's coefficient and preferential attachment (JCPA) model, Jaccard's coefficient and Adamic/Adar (JCAA) model and preferential attachment and Adamic/Adar (PAAA) model are generated with the context of ascertaining more accuracy in the performance of link prediction classifier. The probabilistic model based on Naive Bayes classifier is used as a base classier. Experimental results shows that we have achieved more accuracy in classifier performance which also been verified using receiver operating characteristic (ROC) curve.

Delay‐insensitive identification of neighbors using unslotted and slotted protocols

ABSTRACTFor many applications, it is desirable for a node to be able to identify the neighbor nodes currently within range. However, the identification procedures for terrestrial communication networks (TCNs) are inefficient when implemented in long‐delay networks (LDNs) such as underwater acoustic networks or satellite networks, where the propagation time of a packet cannot be neglected. Here, we propose a time‐efficient and power‐efficient procedure, which is insensitive to propagation delay, for identifying neighbors in an LDN by optimizing the network offered load using either unslotted or slotted protocols. The procedure is adapted to the scenario when node cardinality and distribution are either known or unknown in advance. We achieve improvements as high as 80% in time and 45% in power consumption for our proposed approach compared with approaches developed previously for TCN. Furthermore, we analyze our proposed approach with the inclusion of the capture effect and packet receive time variations. We also provide a closed form formula for finding the optimum guard time and a procedure to estimate the packet receive time variations. Copyright © 2012 John Wiley & Sons, Ltd.

A ring-mesh topology design problem for optical transport networks

This paper deals with a ring-mesh network design problem arising from the deployment of an optical transport network. The problem seeks to find an optimal clustering of traffic demands in the network such that the total cost of optical add-drop multiplexer (OADM) and optical cross-connect (OXC) is minimized, while satisfying the OADM ring capacity constraint, the node cardinality constraint, and the OXC capacity constraint. We formulate the problem as an integer programming model and propose several alternative modeling techniques designed to improve the mathematical representation of the problem. We then develop various classes of valid inequalities to tighten the mathematical formulation of the problem and describe an algorithmic approach that coordinates tailored routines with a commercial solver CPLEX. We also propose an effective tabu search procedure for finding a good feasible solution as well as for providing a good incumbent solution for the column generation based heuristic procedure that enhances the solvability of the problem. Computational results exhibit the viability of the proposed method.

A branch-and-cut algorithm for solving an intraring synchronous optical network design problem

In this paper, we deal with a network design problem arising from the deployment of synchronous optical networks (SONET), a standard of transmission using optical fiber technology. The problem is to find an optimal clustering of traffic demands in the network such that the total number of node assignments (and, hence, add—drop multiplexer equipment requirements) is minimized, while satisfying the ring capacity and node cardinality constraints. This problem can be conceptualized as an edge-capacitated graph partitioning problem with node cardinality constraints. We formulate the problem as a mixed-integer programming model and develop a new branch-and-cut algorithm along with preprocessing routines for optimally solving the problem. We also prescribe an effective heuristic procedure. Promising computational results are obtained using the proposed method. © 2000 John Wiley & Sons, Inc.