Critical Density for Coverage and Connectivity in Three-Dimensional Wireless Sensor Networks Using Continuum Percolation

Notice of Violation of IEEE Publication Principles Critical Density for Coverage and Connectivity in Two-Dimensional Aligned-Orientation Directional Sensor Networks Using Continuum Percolation, by Mohammad Khanjary, Masoud Sabaei, and Mohammad Reza Meybodi in IEEE Sensors Journal, vol. 14, no. 8, pp. 2856-2863, Aug. 2014 After careful and considered review of the content and authorship of this paper by a duly constituted expert committee, this paper has been found to be in violation of IEEE's Publication Principles. This paper contains significant portions of original text from the paper cited below. The original text was copied without attribution (including appropriate references to the original author(s) and/or paper title) and without permission. Integrated Coverage and Connectivity in Wireless Sensor Networks: A Two-Dimensional Percolation Problem, by H. M. Ammari and S. K. Das, in IEEE Transactions on Computers, vol. 57, no. 10, pp. 1423-1434, Oct. 2008 Sensing coverage is one of the fundamental design issues in wireless sensor networks, which reflects the surveillance quality provided by them. Moreover, network connectivity enables the gathered data by sensors to reach to the sink node. Given an initially uncovered field, and as more and more directional sensors are continuously added to the sensor network, the size of partial covered areas increases. At some point, the situation abruptly changes from small fragmented covered areas to a single large covered area. We call this abrupt change the sensing-coverage phase transition (SCPT). Likewise, given an originally disconnected sensor network, as more and more sensors are added, the number of connected components changes such that the sensor network suddenly becomes connected at some point. We call this sudden change the network connectivity phase transition (NCPT). The nature of such phase transitions is a central topic in the percolation theory. In this paper, we introduce aligned-orientation directional sensor networks in which nodes are deployed based on Poisson point process and the orientation of all sensor nodes is the same. Then, we propose an approach to compute density of nodes at critical percolation for both of the SCPT and NCPT problems in such networks, for all angles of field-of-view between 0 and π by using continuum percolation. Due to percolation theory, the critical density is infimum density that for densities above it SCPT and NCPT almost surely occur. In addition, we propose a model for percolation in directional sensor networks, which provides a basis for solving the SCPT and NCPT problems together.

Target Coverage and Network Connectivity in Wireless Sensor Networks (WSNs) plays a momentous role in the field of monitoring environment, habitant observing, disaster recovery, surveillance, etc. Coverage and Network Connectivity collectively can be considered as a proportion of Quality of Service (QoS) in a sensor network. It implies the coverage of each point in the detecting field while in the meantime fulfilling the measure that each node is surrounded by the equivalent neighbourhood of at least one other node. Many primary issues influence the outline and performance of WSN. A Comprehensive survey is made based on the scheduling algorithm and set cover approach, in which we analyze various approaches and their algorithm complexity. Firstly, the scheduling algorithm intermittently provides the required data service with guaranteed efficiency. This methodology can efficiently reduce the entire number of active nodes in the network, resulting in maximizing the network lifetime. Secondly, the set cover approach plays a major role in solving target coverage problem which group sensors into each cover set thereby, target coverage was achieved. Typical issues and open research challenges are addressed by classifying the approaches available in literature into three broad categories namely, adaptable coverage radius, coverage deployment strategy, and sleep scheduling. This survey aims to provide a better perceptive of the existing open challenges and possible futuristic approaches for target coverage and network connectivity in wireless sensor networks.

Toward the end of the 20th century, the Internet has been able to provide a large number of users with the ability to move diverse forms of information readily and thus has revolutionized business, industry, defense, science, education, research, and human interactions. In the last 10 years, sensor networking combines the technology of modern microelectronic sensors, embedded computational processing systems, and modern computer networking methodology. It is believed that sensor networking in the 21st century will be equally significant by providing measurement of the spatial-temporal physical phenomena around us, leading to a better understanding and utilization of this information in a wide range of applications. Sensor networking will be able to bring a finer-grained and fuller measurement and characterization of the world around us to be processed and communicated, so the decision makers can utilize the information to take actions in near-real-time. The potential applications enabled by SNs include security and surveillance, environmental monitoring and control, target detection and tracking, etc. Wireless sensor networks utilize the extensive networking concepts of ad hoc networks and apply them to specific sensor network scenarios. This mini-special issue comprises three papers covering three quiet diverse aspects of wireless sensor networks. The first paper, “Lifetime Maximization Based on Coverage and Connectivity in Wireless Sensor Networks,” is by T. Zhao et al. They studied the problem of network lifetime maximization for QoS specific information retrieval for the reconstruction of a spatially correlated signal field in a wireless sensor network for two wireless transmission cases. In one case, they assumed there exist single-hop transmissions between sensors and the access point, and in the other case, the measurements are sent to the access point through multi-hop transmissions. To address both of these problems, they formulated the problems using integer programming based on the theories of coverage and connectivity in sensor networks and then derived upper bounds for the network lifetime that provides benchmarks for the performance of suboptimal methods. Several lowcomplexity suboptimal algorithms for joint node scheduling and data routing were then proposed to approach the performance upper bounds. The second paper, “Using Heterogeneity to Enhance Random Walk-based Queries,” is by M. Zuniga et al. They presented a study of the impact of heterogeneous node connectivity on random walk-based queries. The main contribution of the work is showing that with a small percentage (e.g., 10%) of high-degree nodes in the network and using a simple distributed push-pull mechanism, significant cost savings can be obtained (e.g., between 30% and 70%) depending on the coverage of the high-degree nodes. Their work provides interesting theoretical results for line topologies showing that when cluster-heads have a coverage of k nodes to the right and left and are uniformly distributed, a fraction of 4/5k J Sign Process Syst (2009) 57:381–383 DOI 10.1007/s11265-009-0377-9

While coverage and geographic forwarding in two- dimensional (2D) wireless sensor networks (WSNs) have been well studied, three-dimensional (3D) WSNs have gained relatively less attention in the literature although real-world applications, such as underwater WSNs, require design in 3D instead of 2D space. Most of geographic forwarding protocols for 2D WSNs, however, assume that all sensors are always awake during forwarding. Such an assumption is not realistic for real-world applications, where sensors are duty-cycled to save energy. In this paper, we propose the first solution to the problem of geographic forwarding in duty-cycled 3D k-covered WSNs, where each point in a 3D field is covered by at least k sensors. First, we analyze the k-coverage problem in 3D WSNs and show that the extension of the analysis in 2D space to 3D space is not straightforward due to the inherent characteristics of the Reuleaux tetrahedron, and propose a new model that guarantees k-coverage for a 3D field. Then, we propose a distributed k-coverage protocol for 3D WSNs. Second, we design a hybrid forwarding protocol for duty-cycled 3D k-covered WSNs, which benefits from the advantages of both deterministic and opportunistic forwarding. Third, we relax some widely used assumptions to promote the use of our joint protocol in real-world scenarios. Finally, we evaluate the performance of our joint protocol. We find a close to perfect match between theoretical and simulation results.

In Wireless Sensor Networks (WSNs), providing full area coverage while maintaining connectivity between the sensors is considered an important issue. Coverage-aware sleep scheduling is an efficient way to optimize the coverage of WSNs while maximizing the energy consumption. On the other hand, clustering can provide an efficient way to achieve high connectivity in WSNs. Despite the close relationship between the coverage problem and the clustering problem, they have been formulated, discussed and evaluated separately. Furthermore, most existing WSN strategies are designed to be applied on Two-Dimensional (2D) fields under an ideal energy consumption model that relies on calculating the Euclidean distance between any pair of sensors. In reality, sensors are mostly deployed in a Three-Dimensional (3D) field in many applications and they do exhibit a discrete energy consumption model that depends on the sensors' status rather than the distance between them. In this paper, we propose a Pareto-based network configuration strategy for 3D WSN s. In the proposed protocol, deciding the status of each sensor in a 3D WSN s is formulated as a single multi-objective minimization problem. The proposed formulation considers the following combined properties: energy efficiency, data delivery reliability, scalability, and full area coverage. The performance of the proposed protocol is tested in 3D WSNs and under a realistic energy consumption model which is based on the characteristics of the Chip con CC2420 radio transceiver data sheet.

Wireless sensor networks are often deployed for data-gathering or monitoring in a geographical region. This paper explains an important issue to maintain the fidelity of the sensed data while minimizing energy usage in the network. Nature inspired computation like evolutionary computation, swarm intelligence etc., which offers practical advantages to the researcher facing difficult optimization problems. The genetic algorithms are used for efficient connectivity and coverage. Single Objective Genetic Algorithms (SOGA) method is used to yield good results in terms of Coverage, but the objective's graph had shown Pareto optimal designs with differing Endurance. However it is attractive to offer Pareto optimal designs to a user willing to settle for a poorer Coverage in order to gain in Endurance, so that the sensor network lasts longer. This explains concept of Multiple Objective Genetic Algorithm (MOGA) and its implementation and results which are compared to those of the SOGA. Endurance and Robustness to deployment inaccuracy tend to work in the same direction. A MOGA was conducted with the Coverage and Robustness as objectives. The main objective of this paper is to propose new Strength Perito Evolutionary Algorithm (SPEA) method along with clustering, this will reduce the distances between the sensor nodes that increase the efficiency of the nodes and also increase the connectivity. This will increase lifetime of sensors and connectivity.

Some problems about the connectivity of wireless sensor networks (WSNs) are always important and difficult topics in research, especially the trade-off between connectivity and energy control. In this paper, we present a novel and effective method to calculate nearest neighbor nodes in three-dimensional WSNs using Poisson point field theory, which enables each node to find the kth nearest neighbor node and adjust transmitting range according to local requirement. Moreover, we derive the probability expression of the k-connected network. Finally, we give corresponding simulation results and discussions about the practical value for node energy control and design of WSNs.

Aiming at the uneven random coverage distribution of wireless sensor networks sensor nodes, the sparrow search algorithm (SSA) is used to optimize the node coverage of wireless sensor networks. To improve the global search capability of SSA, the algorithm is improved and applied to the wireless sensor networks of bridge monitoring. For enhancing the coverage of the wireless sensor networks, this article uses two improved methods. One is to use the good point set theory to make the initial population evenly distributed; another is to introduce a weight factor to speed up its convergence. The experiments have proved the reliability and rationality of the algorithm. The improved algorithm is superior to other meta-heuristic algorithms and provides a new idea for optimizing bridge monitoring wireless sensor networks coverage.

Finding an optimal node deployment strategy in wireless sensor networks (WSNs) that would reduce cost, be robust to node failures, reduce computation, and communication overhead, and guarantee a high level of coverage along with network connectivity is a difficult problem. In fact, sensing coverage and network connectivity are two of the most fundamental problems in WSNs as they can directly impact the network lifetime and operation. In this paper, we consider deriving optimal conditions for connectivity with coverage in WSNs. Most versions of this problem are (NP-complete), while approximation algorithms cannot be developed for some versions of polynomial time, unless P = NP. Hence, we also develop a heuristic for some versions of the problem and the efficacy of the heuristic will be evaluated through extensive simulations. We are also interested in determining the probability of finding a path between a given pair of nodes over a given topology of WSNs. This will serve as a measure of connectivity with coverage of the network. Hence, we derive necessary and sufficient conditions for connectivity with coverage over a clustered structure in WSNs. Then, employing queuing networks modeling techniques, we present a dynamic programming study of the connectivity with coverage of clustered structure and its effect on routing in generalized WSNs. The performance evaluation of the proposed schemes shows that availability of nodes, sensor node coverage, and the connectivity were sufficiently enhanced to maximize network lifetime.

The growth of Wireless Sensor Network (WSN) in the late years, encourages a lot of research in it. The most investigated topics are energy consumption, coverage, and connectivity in WSN. This paper discusses connectivity for WSN with the presence of simple obstacles. The LEACH protocol is used and is modified based on the obstacle, to improve the clustering process. We propose an algorithm based on the intersection of line to improve the original LEACH. The result of simulation shown the modified LEACH algorithm works better than the original LEACH with the presence of obstacle based on energy consumption and loss of transmission data. The future work could be done to modify the LEACH for arbitrary obstacle.

Coverage and connectivity in the 3D surface of sensor nodes as the mountain is a critical problem in a wireless sensor network (WSN). This paper suggests a solution to multi-connectivity deployment WSN coverage based on combining Sailfish optimizer (SFO) with the characteristic of 3D surface topography. The target area divided into mesh grids of a size to establish the multi-connectivity of every grid. The cover set constructed through the direction gradient probabilistic model and connected graph and the joint points to graph within the grid by optimizing SFO. A large number of simulation experiments show that the proposed method can cover the target region and guarantee the connectivity and robustness of the network.

Efficient deployment of Wireless Sensor Networks (WSNs) is critical to ensuring optimal performance across key metrics such as coverage, connectivity, energy efficiency, and network longevity. Traditional deployment strategies such as random, grid-based, and deterministic placements often fail to accommodate heterogeneous node capabilities or adapt to dynamic environmental conditions. This study proposes a Particle Swarm Optimization (PSO)-based deployment framework tailored for heterogeneous WSNs. The framework incorporates intelligent role assignment, metaheuristic optimization, and adaptive maintenance phases to balance coverage quality, minimize energy consumption, and enhance fault tolerance. A comprehensive simulation-based evaluation involving nine deployment strategies demonstrates that the proposed PSO-based approach achieves superior performance, including an average coverage of 91.4 ± 1.8%, extended operational lifetime exceeding 3,400 rounds, and improved connectivity robustness. The framework also exhibits strong scalability and resilience in the presence of node failures. These findings establish the proposed deployment model as a viable solution for real-world, large-scale, and energy-constrained WSN applications.

Efficient coverage and connectivity are two important factors that ensures better service quality especially during tracking targets or monitoring events in wireless sensor network. Although massive amount of studies has been carried out in the past to enhance coverage and connectivity issues, till date very few studies have witnessed a significant and standard outcomes that can opt further. Hence, this paper introduces a computationally efficient technique for jointly addressing both coverage and connectivity problems in large-scale wireless sensor network that ensures optimal network lifetime too. The proposed system has been empirically designed, and algorithms formulated to ensure energy efficient monitoring of event. The outcomes of the study are compared with standard energy efficient hierarchical protocol to benchmark the results.

Reliable network connectivity in wireless sensor networks (WSN) is difficult to achieve. Harsh, unattended, low-security environments and resource-constrained nodes exacerbate the problem. An ability to detect connectivity disruptions, due to either security or environmental problems, allows WSN to conserve power and memory while reducing network congestion. We propose RE2-CD, an integrated solution incorporating both robustness to attack and energy-efficiency. To enhance security, a robust outlier detection algorithm assists nodes in detecting a specific threat in their environment. To improve energy-efficiency, a cluster-based cut detection algorithm recognizes and reacts to disrupted connectivity. Extensive simulations across a range of network sizes and densities indicate that energy-efficiency can be improved by an order of magnitude in denser networks while malicious nodes are detected at deviations of 1% from expected behavior.

Mobile robots improve scalability and performance of wireless sensor networks. Protocols for many services including data collection, localization, topology control and security in wireless sensor networks include mobile robots. Using a single robot limits the scalability and performance and multiple robots are used as a result. When multiple robots are deployed, it is desirable to have the robots connected to provide improved services. However, coordinating the robots optimally to achieve connectivity among them is not trivial. We use computational geometry techniques to achieve connectivity. We use the concept of Frechet distance between curves to synchronize the robots for connectivity. We extend the idea of Frechet distance to multiple curves where each curve is the path of a robot. We analyze the proposed idea theoretically and show that the theory can not be applied directly due to limitations on robot speed and speed changes. Therefore, we propose a practical approach where maximum robot speed is bounded and speed changes is limited. Simulations show that the connectivity among the robots is maintained when the robots follow the movement pattern based on the Frechet distance between the paths of consecutive robots.