A Survey on Deployment and Coverage Strategies in Three-Dimensional Wireless Sensor Networks
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paper_title: 3D Coverage Analysis under Heterogeneous Deployment Strategies in Wireless Sensor Networks

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In this paper, we propose novel deployment strategies for Wireless Sensor Networks and study 3D coverage under these heterogeneous deployment strategies. Our aim is to find answers to questions like how many sensors are needed to cover a specified 3D terrain at a specified coverage percentage. Furthermore, the effect of sleeping on coverage is also studied. Simulation results demonstrate that depending on application requirements an appropriate deployment strategy can be selected to obtain required 3D coverage.
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paper_title: Sink placement on a 3D terrain for border surveillance in wireless sensor networks

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With their distributed nature and redundant operation capability, wireless sensor networks are very suitable for border surveillance scenarios that track intruders trying to breach to a safe side. In such scenarios, keeping the operation going on for as long as possible is the most important aspect of the network. We propose that by placing sink at a carefully selected coordinate will results in a longer living network. We also place restrictions on the candidate locations so that the sensing quality of the network is above a useful predetermined value and the sink is placed in a relatively safe location to avoid destruction. In order to find the suitable coordinates we propose a modified lifetime metric which takes quality and safety measures into account. We also propose a genetic algorithm which uses a discrete event simulator-in-the-loop over a three dimensional terrain to find locations for the sink that fits the given quality and safety restrictions. Using a three dimensional underlying terrain makes the proposed approach more realistic. The results obtained for various sensor network scenarios indicate that the proposed algorithm can find locations that increase the lifetime by also considering the sensing quality and safety.
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paper_title: Three-dimensional sensor network connectivity considering border effects and channel randomness with application to underwater networks

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Connectivity is an important measure that determines the quality of service of a network. The sensor networks that find applications in underwater, terrain and space communication requires the nodes to be three-dimensional (3D), and hence, 3D connectivity is a challenging issue to be addressed. Also, the networks are prone to fading and shadowing effects due to the barriers in the communication path. Hence, the analysis of deterministic connectivity is not valid as the range of connectivity is a randomly varying parameter in the presence of fading and shadowing. In this study, the authors provide an analysis of 3D connectivity under channel randomness considering the border effects, with application to the underwater networks, where the existence of network border is significant due to the presence of natural boundaries at bottom and surface of the ocean. The connectivity analysis in the presence of log-normal shadowing is performed, and closed-form expressions are derived. Also, the 3D connectivity under the combined effects of Rayleigh fading and log-normal shadowing is analysed, which can be approximated to the well-known K-distribution used to characterise underwater sensor networks. The analysis of the proposed work matches almost exactly with the simulation, and thus, the results are validated.
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paper_title: An effective WSN deployment algorithm via search economics

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The development of a powerful search mechanism to find a good solution is the current research direction of studies on metaheuristic algorithms; however, most of the developed mechanisms will search and check the possible solutions without knowledge of the overall landscape of the solution space during the convergence process. To make each search during the convergence process as effective as possible, this paper presents a new metaheuristic algorithm called search economics (SE) to solve the deployment problem of wireless sensor networks. The main distinguishing features of the SE are twofold: the first is its capability to depict the solution space based on the solutions that have been checked by the search algorithm, and second is its capability to use the knowledge thus obtained, i.e., the "landscape of the solution space," during the search process. On the basis of these concepts, the investment in a search process will be more meaningful and thus less easy to fall into a local optimum during early iterations. The experimental results show that the proposed algorithm can provide a result for the deployment problem that is significantly better than those provided by the state-of-the-art metaheuristic algorithms evaluated in this study in terms of the quality.
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paper_title: A distributed scheme for 3D space coverage in tactical underwater sensor networks

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In this paper, a distributed scheme for three dimensional sensor space coverage in tactical underwater sensor networks is introduced. When sensor nodes are first deployed, sensors lie in surface buoys. After deployment, sensors are lowered to various depths selected by our scheme such that the maximum coverage of the three dimensional sensor space is maintained. Experiments show that our scheme maintains more than 90% coverage efficiency most of the time at the expense of acceptable control traffic overhead.
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paper_title: The coverage problem in three-dimensional wireless sensor networks

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One of the fundamental issues in sensor networks is the coverage problem, which reflects how well a sensor network is monitored or tracked by sensors. In this paper, we formulate this problem as a decision problem, whose goal is to determine whether every point in the service area of the sensor network is covered by at least /spl alpha/ sensors, where /spl alpha/ is a given parameter and the sensing regions of the sensors are modeled by balls (not necessarily of the same radius). This problem in a 2D space is solved in (C. F. Huang et al, ACM Int'l W'kshop on Wireless Sensor Networks and App., p.115-12 1, 2003) with an efficient polynomial-time algorithm (in terms of the number of sensors). In this paper, we show that tackling this problem in a 3D space is still feasible within polynomial time. The proposed solution can be easily translated into an efficient polynomial-time distributed protocol.
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paper_title: Improving routing performance of underwater wireless sensor networks

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In this paper we present a 3D node deployment strategy to improve the routing performance of an Underwater Wireless Sensor Network (UWSN). This is done by carefully considering the unique characteristics of underwater acoustic communication as well as three-dimensional (3D) and dynamic nature of Underwater Wireless Sensor Networks (UWSNs). This strategy targets 3D UWSN and not only improves the routing protocol performance in terms of end to end delay and energy consumption but also provides reliability in data transmission and increases network lifetime. This strategy has been developed step by step from a single line of vertical communication to an effective 3D node deployment for UWSN. Several simulation experiments were carried out after adding different features to the final design, in order to observe their impact on the overall routing performance. Improving the routing performance by carefully analyzing the impact of 3D node deployment strategy and ensuring full sensing, transmission and back-up coverage in a highly unpredictable underwater environment, is a novel approach which can be embedded with other networking protocols to improve their performance.
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paper_title: Surface Coverage in Wireless Sensor Networks

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Coverage is a fundamental problem in Wireless Sensor Networks (WSNs). Existing studies on this topic focus on 2D ideal plane coverage and 3D full space coverage. The 3D surface of a targeted Field of Interest is complex in many real world applications; and yet, existing studies on coverage do not produce practical results. In this paper, we propose a new coverage model called surface coverage. In surface coverage, the targeted Field of Interest is a complex surface in 3D space and sensors can be deployed only on the surface. We show that existing 2D plane coverage is merely a special case of surface coverage. Simulations point out that existing sensor deployment schemes for a 2D plane cannot be directly applied to surface coverage cases. In this paper, we target two problems assuming cases of surface coverage to be true. One, under stochastic deployment, how many sensors are needed to reach a certain expected coverage ratio? Two, if sensor deployment can be planned, what is the optimal deployment strategy with guaranteed full coverage with the least number of sensors? We show that the latter problem is NP-complete and propose three approximation algorithms. We further prove that these algorithms have a provable approximation ratio. We also conduct comprehensive simulations to evaluate the performance of the proposed algorithms.
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paper_title: Real-Time Profiling of Fine-Grained Air Quality Index Distribution Using UAV Sensing

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Given significant air pollution problems, air quality index (AQI) monitoring has recently received increasing attention. In this paper, we design a mobile AQI monitoring system boarded on unmanned-aerial-vehicles (UAVs), called ARMS, to efficiently build fine-grained AQI maps in realtime. Specifically, we first propose the Gaussian plume model on basis of the neural network (GPM-NN), to physically characterize the particle dispersion in the air. Based on GPM-NN, we propose a battery efficient and adaptive monitoring algorithm to monitor AQI at the selected locations and construct an accurate AQI map with the sensed data. The proposed adaptive monitoring algorithm is evaluated in two typical scenarios, a two-dimensional open space like a roadside park, and a three-dimensional space like a courtyard inside a building. Experimental results demonstrate that our system can provide higher prediction accuracy of AQI with GPM-NN than other existing models, while greatly reducing the power consumption with the adaptive monitoring algorithm.
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paper_title: Three-dimensional sensor network connectivity considering border effects and channel randomness with application to underwater networks

paper_content:

Connectivity is an important measure that determines the quality of service of a network. The sensor networks that find applications in underwater, terrain and space communication requires the nodes to be three-dimensional (3D), and hence, 3D connectivity is a challenging issue to be addressed. Also, the networks are prone to fading and shadowing effects due to the barriers in the communication path. Hence, the analysis of deterministic connectivity is not valid as the range of connectivity is a randomly varying parameter in the presence of fading and shadowing. In this study, the authors provide an analysis of 3D connectivity under channel randomness considering the border effects, with application to the underwater networks, where the existence of network border is significant due to the presence of natural boundaries at bottom and surface of the ocean. The connectivity analysis in the presence of log-normal shadowing is performed, and closed-form expressions are derived. Also, the 3D connectivity under the combined effects of Rayleigh fading and log-normal shadowing is analysed, which can be approximated to the well-known K-distribution used to characterise underwater sensor networks. The analysis of the proposed work matches almost exactly with the simulation, and thus, the results are validated.
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paper_title: Method Based on Triangulation for Sensor Deployment on 3D Surfaces

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In this work a new method is proposed to obtain the deployment of sensor nodes with a maximum coverage area using a minimum number of sensor nodes in three-dimensional surfaces. The deployment is performed using the dual Delaunay triangulation/Voronoi Diagram. The position selection process considered the vertices as candidate positions and the sensing radius. The positions were selected based on the maximum area coverage and the existence of communication among them. The communication was defined as omnidirectional. To ensure the coverage area, the problem of sensing superposition was considered. The verification of the communication is accomplished by the minimum spanning tree algorithm. To certify the versatility of the proposed method, we show the deployment in distinct surface areas commonly monitored by Wireless Sensor Networks. The results were significant, with coverage area between 84% and 95% for distinct types of reliefs.
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paper_title: A Novel Sensor Deployment Method Based on Image Processing and Wavelet Transform to Optimize the Surface Coverage in WSNs

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A novel sensor deployment method utilize Discrete wavelet transform (DWT) is proposed, and the DWT is used to calculate the sub-band energy entropy to ascertain the coverage cavities in Wireless sensor networks (WSNs). We address the problem of deploying a limit number of sensors to optimize the coverage ratio in 3D surface, while it is a complex surface in space and sensors can be deployed only onto it. Another novel aspect of this paper is that the method followed utilizes an Artificial bee colony algorithm with dynamic search strategy (ABC-DSS), which mimics the behavior of bees, and the new modified ABC-DSS algorithm matches the sensor deployment problems on 3D surface well. The extensive simulations illustrate that comparing with the deployment method based on Particle swarm optimization (PSO) and ABC, the ABC-DSS which utilizes the wavelet sub-band energy entropy is functional and efficient on 3D surface deployment problems.
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paper_title: Information Estimation with Node Placement Strategy in 3D Wireless Sensor Networks

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The cluster formation in three-dimensional wireless sensor networks (3D-WSN) gives rise to overlapping of signals due to spherical sensing range which leads to information redundancy in the network. To address this problem, we develop a sensing algorithm for 3D-WSN based on dodecahedron topology which we call three-dimensional distributed clustering (3D-DC) algorithm. Using 3D-DC algorithm in 3D-WSN, accurate information extraction appears to be a major challenge due to the environmental noise where a cluster head (CH) node gathers and estimates information in each dodecahedron cluster. Hence, to extract precise information in each dodecahedron cluster, we propose three-dimensional information estimation (3D-IE) algorithm. Moreover, node deployment strategy also plays an important factor to maximize information accuracy in 3D-WSN. In most cases, sensor nodes are deployed deterministically or randomly. But both the deployment scenarios are not aware of where to exactly place the sensor nodes to extract more information in terms of accuracy. Therefore, placing nodes in its appropriate positions in 3D-WSN is a challenging task. We propose a three-dimensional node placement (3D-NP) algorithm which can find the possible nodes and their deployment strategy to maximize information accuracy in the network. We perform simulations using MATLAB to validate the 3D-DC, 3D-IE and 3D-NP, algorithms, respectively.
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paper_title: A Novel Deployment Scheme Based on Three-Dimensional Coverage Model for Wireless Sensor Networks

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Coverage pattern and deployment strategy are directly related to the optimum allocation of limited resources for wireless sensor networks, such as energy of nodes, communication bandwidth, and computing power, and quality improvement is largely determined by these for wireless sensor networks. A three-dimensional coverage pattern and deployment scheme are proposed in this paper. Firstly, by analyzing the regular polyhedron models in three-dimensional scene, a coverage pattern based on cuboids is proposed, and then relationship between coverage and sensor nodes' radius is deduced; also the minimum number of sensor nodes to maintain network area's full coverage is calculated. At last, sensor nodes are deployed according to the coverage pattern after the monitor area is subdivided into finite 3D grid. Experimental results show that, compared with traditional random method, sensor nodes number is reduced effectively while coverage rate of monitor area is ensured using our coverage pattern and deterministic deployment scheme.
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paper_title: Location Optimization of Wireless Sensor Network in Intelligent Workshop Based on the Three-Dimensional Adaptive Fruit Fly Optimization Algorithm

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The production process of modern manufacturing industry is complex and changeable, manufacturing resources have extensive dynamic characteristics. For effectively managing and controlling manufacturing resources, realizing real-time location data collection of intelligent workshop, a manufacturing resource location sensing architecture based on the wireless sensor network is proposed. For en-suring real-time accuracy of manufacturing resource location data in the intelligent workshop, a three-dimensional adaptive fruit fly optimization algorithm is de-signed to estimate the location coordinates, the new algorithm introduced the adaptive inertial weight coefficient, retained the advantage of strong local search ability of fruit fly optimization algorithm, improved the ability of global optimiza-tion, effectively solved the problem of three-dimensional location in intelligent workshop. The simulation results show that, the algorithm in this paper is applied to the location calculation of triangulation, which has smaller location error and shorter operation time, it improves the accuracy of the location data and meets the real-time location requirements of manufacturing resources such as intelligent workshop staff, materials, logistics vehicles etc. facilitate resource sensing and scheduling management, thereby improving management standards and product quality.
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paper_title: 3D Self-Deployment Algorithm in Mobile Wireless Sensor Networks

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The sensor deployment problem of wireless sensor networks (WSNs) is a key issue in the researches and the applications of WSNs. Fewer works focus on the 3D autonomous deployment. Aimed at the problem of sensor deployment in three-dimensional spaces, the 3D self-deployment (3DSD) algorithm in mobile sensor networks is proposed. A 3D virtual force model is utilized in the 3DSD method. A negotiation tactic is introduced to ensure network connectivity, and a density control strategy is used to balance the node distribution. The proposed algorithm can fulfill the nodes autonomous deployment in 3D space with obstacles. Simulation results indicate that the deployment process of 3DSD is relatively rapid and the nodes are well distributed. Furthermore, the coverage ratio of 3DSD approximates the theoretical maximum value.
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paper_title: Improving routing performance of underwater wireless sensor networks

paper_content:

In this paper we present a 3D node deployment strategy to improve the routing performance of an Underwater Wireless Sensor Network (UWSN). This is done by carefully considering the unique characteristics of underwater acoustic communication as well as three-dimensional (3D) and dynamic nature of Underwater Wireless Sensor Networks (UWSNs). This strategy targets 3D UWSN and not only improves the routing protocol performance in terms of end to end delay and energy consumption but also provides reliability in data transmission and increases network lifetime. This strategy has been developed step by step from a single line of vertical communication to an effective 3D node deployment for UWSN. Several simulation experiments were carried out after adding different features to the final design, in order to observe their impact on the overall routing performance. Improving the routing performance by carefully analyzing the impact of 3D node deployment strategy and ensuring full sensing, transmission and back-up coverage in a highly unpredictable underwater environment, is a novel approach which can be embedded with other networking protocols to improve their performance.
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paper_title: Mountainous terrain coverage in mobile sensor networks

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The sensing field on three-dimensional (3D) terrains that is supposed to be fully covered by deployed nodes may not be covered because of random aerial deployment. Non-uniform coverage has a negative impact upon that their lifetime and performance get short and worse, respectively. Mobile sensor networks (MSNs) are introduced to improve a coverage problem from sensor malfunction by an obstacle or the terrestrial environment. Providing coverage in a mountainous terrain has become critical issues in MSNs. This work proposes a 3D coverage method that can consider a physical feature, such as slope, in a mountainous terrain, that is, a 3D spiral model that allows mobile sensors to move freely in spiral lines devised using the height and radius of a concaved terrain. In the proposed model, the reasonable number of sensors to be deployed and the designated sensing points achieve full coverage. This paper focuses on full coverage for which the spiral model challenges the reasonability in the number of sensors. The experimental results show that the proposed method provides improved performance in terms of coverage ratios and expected coverage time; in addition, this has higher accuracy in lower power cost and better expansibility.
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paper_title: Analyzing the redeployment problem of mobile wireless sensor networks via geographic models

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Since sensor networks integrate virtual and physical worlds, spatial deployment of sensor nodes may have a significant impact on operation costs and performance. This paper investigates the problem of redeploying mobile sensor networks, in which the objective is to design an efficient algorithm which optimizes the global performance of networks. We take a novel approach in analyzing the problem from a macroscopic perspective, modeling the sensor deployment as a density distribution and the redeployment algorithm as an integral transform of that distribution. Despite lacking the details for individual node, we may still derive insightful results, such as number of moves, stability, and transitional behavior. We also derive the bound of total moving distance difference between an arbitrary one-move algorithm and the optimum redeployment algorithm, allowing for the estimation of the minimum moving distance from the initial deployment region. In summary, we present an theoretical analysis of the redeployment problem from a macroscopic perspective, and believe the results can serve as a basis for further algorithm development and analysis. Copyright © 2011 John Wiley & Sons, Ltd.
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paper_title: Probabilistic Sensing Model for Sensor Placement Optimization Based on Line-of-Sight Coverage

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This paper proposes a probabilistic sensor model for the optimization of sensor placement. Traditional schemes rely on simple sensor behaviour and environmental factors. The consequences of these oversimplifications are unrealistic simulation of sensor performance and, thus, suboptimal sensor placement. In this paper, we develop a novel probabilistic sensing model for sensors with line-of-sight-based coverage (e.g., cameras) to tackle the sensor placement problem for these sensors. The probabilistic sensing model consists of membership functions for sensing range and sensing angle, which takes into consideration sensing capacity probability as well as critical environmental factors such as terrain topography. We then implement several optimization schemes for sensor placement optimization, including simulated annealing, limited-memory Broyden-Fletcher-Goldfarb-Shanno method, and covariance matrix adaptation evolution strategy.
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paper_title: Connected Coverage in Three-Dimensional Wireless Sensor Networks Using Convex Polyhedral Space-Fillers

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The coverage problem of a three-dimensional (3D) space has similarity with the tiling problem in the same space, which can be formulated as follows: How can a 3D space be tiled by replicas of tiles? This is an instance of the second part of Hilbert's eighteenth problem [14], which is stated as follows: "What convex polyhedra exist for which a complete filling of all space is possible by juxtaposition of congruent copies?" In this paper, we propose a polyhedral framework to investigate the connected coverage problem in 3D homogeneous wireless sensor networks. First, we restrict the sensors' sensing sphere to a variety of convex polyhedral space-fillers. Our study aims to find the largest enclosed convex polyhedron space-filler in the sensors' sensing sphere, with a goal to maximize their utilized sensing volume. Second, based on this analysis, we select a minimum number of sensors to cover a 3D space for deterministic and random sensor deployment strategies. Third, we compute the ratio of the communication range to the sensing range of the sensors to ensure network connectivity. Fourth, we corroborate our analysis with various simulation results.
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paper_title: A novel coverage algorithm based on 3D-Voronoi cell for underwater wireless sensor networks

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This paper studies the three-dimensional coverage of an underwater wireless sensor network (UWSN) consisting of anchored nodes. As anchored nodes are first randomly deployed on the ocean surface and can only move in the z-axis direction, we propose a two-stage node selection and sinking scheme to maximize the network coverage. In the first stage, we adopt a minimum cost perfect matching of a weighted complete bipartite graph to select the optimal sinking nodes to ideal pattern locations. After the first stage, some coverage holes may exist due to the limited mobility of anchored nodes. In the second stage, we then propose a coverage hole and repairing algorithm based on the three-dimensional Voronoi diagram and a clustering algorithm to further sink the remaining nodes. Simulation results validate the effectiveness of the proposed algorithm, and it can achieve higher coverage ratio with the same number of nodes, compared with an existing peer algorithm.
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paper_title: Covering a 3D flat surface with autonomous and mobile wireless sensor nodes

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Wireless Sensor Networks (WSNs) are used in a wide range of applications due to their monitoring and tracking abilities. Depending on the applications goals, sensor nodes are deployed either in a two dimensional (2D) area or in a three-dimensional (3D) area. In addition, WSN deployment can be either in a distributed or a centralized manner. In this paper, we are interested in a fully distributed deployment of WSN in several 3D-flat-surface configurations using autonomous and mobile nodes. Our goal is to ensure full 3D flat surfaces coverage and maintain network connectivity for these surfaces. To reach our goal we propose 3D-DVFA-FSC, a distributed deployment algorithm based on virtual forces strategy to move sensor nodes over different 3D-flat-surface shapes. Simulation results show that 3D-DVFA-FSC provides a full coverage rate regardless of the 3D-flat-surface configuration while maintaining network connectivity.
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paper_title: Probability-Based Coverage Algorithm for 3D Wireless Sensor Networks

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We propose a probability-based K-coverage control approach (PKCCA) for the contradiction between the inherent uncertainty and strong fault-tolerance ability and robustness of wireless sensor networks in the monitoring of three-dimensional space. The entire monitoring region is to be covered by at least K sensors with probability T. A grid distribution and greedy heuristic are introduced to determine the best placement of sensors. Our approach will be terminated when a preset upper limit on the number of sensors is reached, or the coverage task is completed. We implement our approach and compare it against traditional random and uniform deployment. The results show that PKCCA uses less sensors to complete the same coverage task or same sensors to reach higher coverage degree. We also analyze the cases of preferential coverage for sub-regions. PKCCA is a better solution with high reliability and robustness to detect special environment with weak propagation of signal.
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paper_title: Convex Polyhedral Space-Fillers Based Connected k-Coverage in Three-Dimensional Wireless Sensor Networks

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The problem of coverage in three-dimensional (3D) wireless sensor networks is challenging and hard. In this paper, we focus on the problem of k-coverage of a 3D field of interest (FoI), where every point is covered by at least k sensors. First, we propose three sensor placement strategies to guarantee k-coverage of a 3D FoI. Second, we compute the corresponding sensor density. Third, we investigate the ratio of the radius of the communication range of the sensors to the radius of their sensing range. Our study is based on polyhedral convex spacefillers. It shows that the great rhombicuboctahedron is the best 3D space-filler with respect to the coverage quality metric. We corroborate our analysis with various simulation results.
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paper_title: 3D-kCov-ComFor: An Energy-Efficient Framework for Composite Forwarding in Three-Dimensional Duty-Cycled k-Covered Wireless Sensor Networks

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Most existing work on coverage, connectivity, and geographic forwarding considers a two-dimensional (2D) space, where the sensors are deployed in a 2D field. However, there are several cases where the 2D assumption is not valid for the design of those types of wireless sensor networks (WSNs), such as underwater sensor deployment and sensors deployed on the trees of different heights in a forest. In this article, we investigate the problem of k-coverage in three-dimensional (3D) WSNs, where each point in a 3D field is covered by at least k sensors simultaneously. Moreover, it is commonly assumed in most of the work on the problem of geographic forwarding in WSNs that all the sensors are always on (or active) during the network operational lifetime, and, particularly, during data forwarding. However, this type of design is neither practical nor efficient for the sensors whose energy is crucial and limited. Therefore, we consider geographic forwarding in 3D duty-cycled k-covered WSNs, where the sensors can switch between on and off states (i.e., duty-cycled sensors) to save energy. First, we provide a rigorous analysis of the k-coverage problem in 3D WSNs using Helly's Theorem and the Reuleaux tetrahedron model, and compute the sensor spatial density to k-cover a 3D field. Second, based on this analysis, we compute a lower bound and an upper bound on the number of overlapping Reuleaux tetrahedra that are necessary to fill a 3D convex shape, such as the sensing sphere of a sensor. Third, using these results, we present a localized (i.e., based on local information of one-hop neighbors), pseudo-distributed (i.e., not fully distributed) protocol to achieve k-coverage of a 3D field with a reduced number of active sensors, while ensuring connectivity between them. Fourth, we discuss our composite geographic forwarding protocol for 3D duty-cycled k-covered WSNs using a combination of deterministic and opportunistic schemes to forward sensed data towards the sink. We will study the problem of 3D space filling (or space covering) in the context of the above-mentioned problems in 3D WSNs. Fifth, we relax two widely used assumptions, namely sensor homogeneity and sensing range convexity, to generalize our k-coverage protocol in 3D space. Last, we show several simulation results of our framework for joint k-coverage and composite geographic forwarding in 3D duty-cycled WSNs, called 3D-kCov-ComFor. We found a close-to-perfect match between our theoretical and simulation results.
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Title: A Survey on Deployment and Coverage Strategies in Three-Dimensional Wireless Sensor Networks

Section 1: INTRODUCTION
Description 1: Outline the importance of 3D Wireless Sensor Networks (WSNs), discussing fundamental issues such as coverage problems, deployment strategies, and the unique challenges associated with three-dimensional environments.

Section 2: Recent Research Work
Description 2: Summarize key research contributions and recent advancements in the deployment and coverage strategies for 3D WSNs.

Section 3: 3D DEPLOYMENT STRATEGIES
Description 3: Explain the importance of sensor deployment in WSNs and categorize the different deployment methods into static and dynamic schemes.

Section 4: Deployment Problem
Description 4: Describe the challenges and computational complexity associated with the deployment of WSNs in a 3D terrain and discuss various research methods for addressing these issues.

Section 5: COVERAGE PATTERN
Description 5: Discuss the difficulty of solving 3D coverage problems compared to 2D, presenting mathematical models and geometric theories used in existing research.

Section 6: Binary Sensing Model
Description 6: Define and explain the binary sensing model, including its assumptions and mathematical representation.

Section 7: Probabilistic Sensing Models
Description 7: Discuss the probabilistic sensing model, emphasizing its practical applications and advantages over the binary sensing model.

Section 8: Volumetric Quotient-Based Approach
Description 8: Explain the space filling polyhedron approach, detailing various types of polyhedrons used for 3D space coverage.

Section 9: Spherical Overlap Approach (k-coverage)
Description 9: Describe the spherical overlap approach, including k-coverage algorithms and significant contributions in the literature using this method.

Section 10: CONCLUSION
Description 10: Provide a summary of the discussed topics, highlighting the deployment strategies, coverage models, current challenges, and potential future research directions in 3D WSNs.