Coverage Problem in Wireless Sensor Network: A Survey
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paper_title: The coverage problem in a wireless sensor network

paper_content:

One fundamental issue 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 k sensors, where k is a predefined value. The sensing ranges of sensors can be unit disks or non-unit disks. We present polynomial-time algorithms, in terms of the number of sensors, that can be easily translated to distributed protocols. The result is a generalization of some earlier results where only k=1 is assumed. Applications of the result include: (i) positioning applications, (ii) situations which require stronger environmental monitoring capability, and (iii) scenarios which impose more stringent fault-tolerant capability.
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paper_title: Coverage in Hybrid Mobile Sensor Networks

paper_content:

This paper considers the coverage problem for hybrid networks which comprise both static and mobile sensors. The mobile sensors in our network only have limited mobility, i.e., they can move only once over a short distance. In random static sensor networks, sensor density should increase as O(log L + k log log L) to provide k-coverage in a network with a size of L. As an alternative, an all-mobile network can provide k-coverage with a constant density of O(k), independent of network size L. We show that the maximum distance for mobile sensors is O( 1/radic(k) log 3/4(kL)). We then propose a hybrid network structure, comprising static sensors and a small fraction of O( 1/radic(k)) of mobile sensors. For this network structure, we prove that k-coverage is also achievable with a constant sensor density of O(k). Furthermore, for this hybrid structure, we prove that the maximum distance which any mobile sensor has to move is bounded as O(log(3/4)L). We then propose a distributed relocation algorithm, where each mobile sensor only requires local information in order to optimally relocate itself. We verify our analysis via extensive numerical evaluations and show an implementation of the mobility algorithm on real mobile sensor platforms.
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paper_title: The coverage problem in a wireless sensor network

paper_content:

One fundamental issue 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 k sensors, where k is a predefined value. The sensing ranges of sensors can be unit disks or non-unit disks. We present polynomial-time algorithms, in terms of the number of sensors, that can be easily translated to distributed protocols. The result is a generalization of some earlier results where only k=1 is assumed. Applications of the result include: (i) positioning applications, (ii) situations which require stronger environmental monitoring capability, and (iii) scenarios which impose more stringent fault-tolerant capability.
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paper_title: Maintaining Sensing Coverage and Connectivity in Large Sensor Networks

paper_content:

In this paper, we address the issues of maintaining sensing coverage and connectivity by keeping a minimum number of sensor nodes in the active mode in wireless sensor networks. We investigate the relationship between coverage and connectivity by solving the following two sub-problems. First, we prove that if the radio range is at least twice the sensing range, complete coverage of a convex area implies connectivity among the working set of nodes. Second, we derive, under the ideal case in which node density is sufficiently high, a set of optimality conditions under which a subset of working sensor nodes can be chosen for complete coverage. Based on the optimality conditions, we then devise a decentralized density control algorithm, Optimal Geographical Density Control (OGDC), for density control in large scale sensor networks. The OGDC algorithm is fully localized and can maintain coverage as well as connectivity, regardless of the relationship between the radio range and the sensing range. Ns-2 simulations show that OGDC outperforms existing density control algorithms [25, 26, 29] with respect to the number of working nodes needed and network lifetime (with up to 50% improvement), and achieves almost the same coverage as the algorithm with the best result.
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paper_title: On k-coverage in a mostly sleeping sensor network

paper_content:

Sensor networks are often desired to last many times longer than the active lifetime of individual sensors. This is usually achieved by putting sensors to sleep for most of their lifetime. On the other hand, event monitoring applications require guaranteed k-coverage of the protected region at all times. As a result, determining the appropriate number of sensors to deploy that achieves both goals simultaneously becomes a challenging problem. In this paper, we consider three kinds of deployments for a sensor network on a unit square--a √n × √n grid, random uniform (for all n points), and Poisson (with density n). In all three deployments, each sensor is active with probability p, independently from the others. Then, we claim that the critical value of the function npπ r2/ log(np) is 1 for the event of k-coverage of every point. We also provide an upper bound on the window of this phase transition. Although the conditions for the three deployments are similar, we obtain sharper bounds for the random deployments than the grid deployment, which occurs due to the boundary condition. In this paper, we also provide corrections to previously published results. Finally, we use simulation to show the usefulness of our analysis in real deployment scenarios.
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paper_title: Constrained coverage for mobile sensor networks

paper_content:

We consider the problem of self-deployment of a mobile sensor network. We are interested in a deployment strategy that maximizes the area coverage of the network with the constraint that each of the nodes has at least K neighbors, where K is a user-specified parameter. We propose an algorithm based on artificial potential fields which is distributed, scalable and does not require a prior map of the environment. Simulations establish that the resulting networks have the required degree with a high probability, are well connected and achieve good coverage. We present analytical results for the coverage achievable by uniform random and symmetrically tiled network configurations and use these to evaluate the performance of our algorithm.
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paper_title: Integrated coverage and connectivity configuration for energy conservation in sensor networks

paper_content:

An effective approach for energy conservation in wireless sensor networks is scheduling sleep intervals for extraneous nodes while the remaining nodes stay active to provide continuous service. For the sensor network to operate successfully, the active nodes must maintain both sensing coverage and network connectivity. Furthermore, the network must be able to configure itself to any feasible degree of coverage and connectivity in order to support different applications and environments with diverse requirements. This article presents the design and analysis of novel protocols that can dynamically configure a network to achieve guaranteed degrees of coverage and connectivity. This work differs from existing connectivity or coverage maintenance protocols in several key ways. (1) We present a Coverage Configuration Protocol (CCP) that can provide different degrees of coverage requested by applications. This flexibility allows the network to self-configure for a wide range of applications and (possibly dynamic) environments. (2) We provide a geometric analysis of the relationship between coverage and connectivity. This analysis yields key insights for treating coverage and connectivity within a unified framework; in sharp contrast to several existing approaches that address the two problems in isolation. (3) We integrate CCP with SPAN to provide both coverage and connectivity guarantees. (4) We propose a probabilistic coverage model and extend CCP to provide probabilistic coverage guarantees. We demonstrate the capability of our protocols to provide guaranteed coverage and connectivity configurations through both geometric analysis and extensive simulations.
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paper_title: Energy-efficient communication protocol for wireless microsensor networks

paper_content:

Wireless distributed microsensor systems will enable the reliable monitoring of a variety of environments for both civil and military applications. In this paper, we look at communication protocols, which can have significant impact on the overall energy dissipation of these networks. Based on our findings that the conventional protocols of direct transmission, minimum-transmission-energy, multi-hop routing, and static clustering may not be optimal for sensor networks, we propose LEACH (Low-Energy Adaptive Clustering Hierarchy), a clustering-based protocol that utilizes randomized rotation of local cluster based station (cluster-heads) to evenly distribute the energy load among the sensors in the network. LEACH uses localized coordination to enable scalability and robustness for dynamic networks, and incorporates data fusion into the routing protocol to reduce the amount of information that must be transmitted to the base station. Simulations show the LEACH can achieve as much as a factor of 8 reduction in energy dissipation compared with conventional outing protocols. In addition, LEACH is able to distribute energy dissipation evenly throughout the sensors, doubling the useful system lifetime for the networks we simulated.
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paper_title: Stochastic coverage in heterogeneous sensor networks

paper_content:

We study the problem of coverage in planar heterogeneous sensor networks. Coverage is a performance metric that quantifies how well a field of interest is monitored by the sensor deployment. To derive analytical expressions of coverage for heterogeneous sensor networks, we formulate the coverage problem as a set intersection problem, a problem studied in integral geometry. Compared to previous analytical results, our formulation allows us to consider a network model where sensors are deployed according to an arbitrary stochastic distribution; sensing areas of sensors need not follow the unit disk model but can have any arbitrary shape; sensors need not have an identical sensing capability. Furthermore, our formulation does not assume deployment of sensors over an infinite plane and, hence, our derivations do not suffer from the border effect problem arising in a bounded field of interest. We compare our theoretical results with the spatial Poisson approximation that is widely used in modeling coverage. By computing the Kullback-Leibler and total variation distance between the probability density functions derived via our theoretical results, the Poisson approximation, and the simulation, we show that our formulas provide a more accurate representation of the coverage in sensor networks. Finally, we provide examples of calculating network parameters such as the network size and sensing range in order to achieve a desired degree of coverage.
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paper_title: Minimal and maximal exposure path algorithms for wireless embedded sensor networks

paper_content:

Sensor networks not only have the potential to change the way we use, interact with, and view computers, but also the way we use, interact with, and view the world around us. In order to maximize the effectiveness of sensor networks, one has to identify, examine, understand, and provide solutions for the fundamental problems related to wireless embedded sensor networks. We believe that one of such problems is to determine how well the sensor network monitors the instrumented area. These problems are usually classified as coverage problems. There already exist several methods that have been proposed to evaluate a sensor network's coverage.We start from one of such method and provide a new approach to complement it. The method of using the minimal exposure path to quantify coverage has been optimally solved using a numerical approximation approach. The minimal exposure path can be thought of as the worst-case coverage of a sensor network. Our first goal is to develop an efficient localized algorithm that enables a sensor network to determine its minimal exposure path. The theoretical highlight of this paper is the closed-form solution for minimal exposure in the presence of a single sensor. This solution is the basis for the new and significantly faster localized approximation algorithm that reduces the theoretical complexity of the previous algorithm. On the other hand, we introduce a new coverage problem - the maximal exposure path - which is in a sense the best-case coverage path for a sensor network. We prove that the maximal exposure path problem is NP-hard, and thus, we provide heuristics to generate approximate solutions.In addition, we demonstrate the effectiveness of our algorithms through several simulations. In the case of the minimal single-source minimal exposure path, we use variational calculus to determine exact solutions. For the case of maximal exposure, we use networks with varying numbers of sensors and exposure models.
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paper_title: Coverage problems in wireless ad-hoc sensor networks

paper_content:

Wireless ad-hoc sensor networks have recently emerged as a premier research topic. They have great long-term economic potential, ability to transform our lives, and pose many new system-building challenges. Sensor networks also pose a number of new conceptual and optimization problems. Some, such as location, deployment, and tracking, are fundamental issues, in that many applications rely on them for needed information. We address one of the fundamental problems, namely coverage. Coverage in general, answers the questions about quality of service (surveillance) that can be provided by a particular sensor network. We first define the coverage problem from several points of view including deterministic, statistical, worst and best case, and present examples in each domain. By combining the computational geometry and graph theoretic techniques, specifically the Voronoi diagram and graph search algorithms, we establish the main highlight of the paper-optimal polynomial time worst and average case algorithm for coverage calculation. We also present comprehensive experimental results and discuss future research directions related to coverage in sensor networks.
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paper_title: Exposure in wireless Ad-Hoc sensor networks

paper_content:

Wireless ad-hoc sensor networks will provide one of the missing connections between the Internet and the physical world. One of the fundamental problems in sensor networks is the calculation of coverage. Exposure is directly related to coverage in that it is a measure of how well an object, moving on an arbitrary path, can be observed by the sensor network over a period of time. In addition to the informal definition, we formally define exposure and study its properties. We have developed an efficient and effective algorithm for exposure calculation in sensor networks, specifically for finding minimal exposure paths. The minimal exposure path provides valuable information about the worst case exposure-based coverage in sensor networks. The algorithm works for any given distribution of sensors, sensor and intensity models, and characteristics of the network. It provides an unbounded level of accuracy as a function of run time and storage. We provide an extensive collection of experimental results and study the scaling behavior of exposure and the proposed algorithm for its calculation.
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paper_title: Stochastic coverage in heterogeneous sensor networks

paper_content:

We study the problem of coverage in planar heterogeneous sensor networks. Coverage is a performance metric that quantifies how well a field of interest is monitored by the sensor deployment. To derive analytical expressions of coverage for heterogeneous sensor networks, we formulate the coverage problem as a set intersection problem, a problem studied in integral geometry. Compared to previous analytical results, our formulation allows us to consider a network model where sensors are deployed according to an arbitrary stochastic distribution; sensing areas of sensors need not follow the unit disk model but can have any arbitrary shape; sensors need not have an identical sensing capability. Furthermore, our formulation does not assume deployment of sensors over an infinite plane and, hence, our derivations do not suffer from the border effect problem arising in a bounded field of interest. We compare our theoretical results with the spatial Poisson approximation that is widely used in modeling coverage. By computing the Kullback-Leibler and total variation distance between the probability density functions derived via our theoretical results, the Poisson approximation, and the simulation, we show that our formulas provide a more accurate representation of the coverage in sensor networks. Finally, we provide examples of calculating network parameters such as the network size and sensing range in order to achieve a desired degree of coverage.
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paper_title: Designing localized algorithms for barrier coverage

paper_content:

Global barrier coverage that requires much fewer sensors than full coverage, is known to be an appropriate model of coverage for movement detection applications such as intrusion detection. However, it has been proved that given a sensor deployment, sensors can not locally determine whether the deployment provides global barrier coverage, making it impossible to develop localized algorithms, thus limiting its use in practice. In this paper, we introduce the concept of local barrier coverage to address this limitation. Motivated by the observation that movements are likely to follow a shorter path in crossing a belt region, local barrier coverage guarantees the detection of all movements whose trajectory is confined to a slice of the belt region of deployment. We prove that it is possible for individual sensors to locally determine the existence of local barrier coverage, even when the region of deployment is arbitrarily curved. Although local barrier coverage does not always guarantee global barrier coverage, we show that for thin belt regions, local barrier coverage almost always provides global barrier coverage. To demonstrate that local barrier coverage can be used to design localized algorithms, we develop a novel sleep-wakeup algorithm for maximizing the network lifetime, called Localized Barrier Coverage Protocol (LBCP). We show that LBCP provides close to optimalenhancement in network lifetime, while providing global barrier coverage most of the time. It outperforms an existing algorithm called Randomized Independent Sleeping (RIS) by up to 6 times.
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paper_title: Coverage in Hybrid Mobile Sensor Networks

paper_content:

This paper considers the coverage problem for hybrid networks which comprise both static and mobile sensors. The mobile sensors in our network only have limited mobility, i.e., they can move only once over a short distance. In random static sensor networks, sensor density should increase as O(log L + k log log L) to provide k-coverage in a network with a size of L. As an alternative, an all-mobile network can provide k-coverage with a constant density of O(k), independent of network size L. We show that the maximum distance for mobile sensors is O( 1/radic(k) log 3/4(kL)). We then propose a hybrid network structure, comprising static sensors and a small fraction of O( 1/radic(k)) of mobile sensors. For this network structure, we prove that k-coverage is also achievable with a constant sensor density of O(k). Furthermore, for this hybrid structure, we prove that the maximum distance which any mobile sensor has to move is bounded as O(log(3/4)L). We then propose a distributed relocation algorithm, where each mobile sensor only requires local information in order to optimally relocate itself. We verify our analysis via extensive numerical evaluations and show an implementation of the mobility algorithm on real mobile sensor platforms.
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paper_title: Estimating coverage holes and enhancing coverage in mixed sensor networks

paper_content:

Area coverage is one of the most fundamental problems in ad hoc wireless sensor networks because it directly relates to optimization of resources in a sensing field. Maximizing the coverage area while maintaining a lower cost of deployment has always been a challenge, especially when the monitoring region is unknown and possibly hazardous. In this paper, we present a method to deterministically estimate the exact amount of coverage holes under random deployment using Voronoi diagrams and use the static nodes to collaborate and estimate the number of additional mobile nodes needed to be deployed and relocated to optimal positions to maximize coverage. We follow a two-step deployment process in a mixed sensor network and we argue by simulation and analysis that our collaborative coverage enhancing algorithm (COVEN) can achieve a tradeoff between the cost of deployment and percentage of area covered.
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paper_title: Reconfiguration methods for mobile sensor networks

paper_content:

Motion may be used in sensor networks to change the network configuration for improving the sensing performance. We consider the problem of controlling motion in a distributed manner for a mobile sensor network for a specific form of motion capability. Mobility itself may have a high resource overhead, hence we exploit motility, a constrained form of mobility, which has very low overheads but provides significant reconfiguration potential. We present an architecture that allows each node in the network to learn the medium and phenomenon characteristics. We describe a quantitative metric for sensing performance that is concretely tied to real sensor and medium characteristics, rather than assuming an abstract range based model. The problem of determining the desirable network configuration is expressed as an optimization of this metric. We present a distributed optimization algorithm which computes a desirable network configuration, and adapts it to environmental changes. The relationship of the proposed algorithm to simulated annealing and incremental subgradient descent based methods is discussed. A key property of our algorithm is that convergence to a desirable configuration can be proved even though no global coordination is involved. A network protocol to implement this algorithm is discussed, followed by simulations and experiments on a laboratory test bed.
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paper_title: Movement-assisted sensor deployment

paper_content:

Sensor deployment is an important issue in designing sensor networks. We design and evaluate distributed self-deployment protocols for mobile sensors. After discovering a coverage hole, the proposed protocols calculate the target positions of the sensors where they should move. We use Voronoi diagrams to discover the coverage holes and design three movement-assisted sensor deployment protocols, VEC (vector-based), VOR (Voronoi-based), and minimax based on the principle of moving sensors from densely deployed areas to sparsely deployed areas. Simulation results show that our protocols can provide high coverage within a short deploying time and limited movement.
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paper_title: Mobility improves coverage of sensor networks

paper_content:

Previous work on the coverage of mobile sensor networks focuses on algorithms to reposition sensors in order to achieve a static configuration with an enlarged covered area. In this paper, we study the dynamic aspects of the coverage of a mobile sensor network that depend on the process of sensor movement. As time goes by, a position is more likely to be covered; targets that might never be detected in a stationary sensor network can now be detected by moving sensors. We characterize the area coverage at specific time instants and during time intervals, as well as the time it takes to detect a randomly located stationary target. Our results show that sensor mobility can be exploited to compensate for the lack of sensors and improve network coverage. For mobile targets, we take a game theoretic approach and derive optimal mobility strategies for sensors and targets from their own perspectives.
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paper_title: A framework for multi-robot node coverage in sensor networks

paper_content:

Area coverage is a well-known problem in robotics. Extensive research has been conducted for the single robot coverage problem in the past decades. More recently, the research community has focused its attention on formulations where multiple robots are considered. In this paper, a new formulation of the multi-robot coverage problem is proposed. The novelty of this work is the introduction of a sensor network, which cooperates with the team of robots in order to provide coordination. The sensor network, taking advantage of its distributed nature, is responsible for both the construction of the path and for guiding the robots. The coverage of the environment is achieved by guaranteeing the reachability of the sensor nodes by the robots. Two distributed algorithms for path construction are discussed. The first aims to speed up the construction process exploiting a concurrent approach. The second aims to provide an underlying structure for the paths by building a Hamiltonian path and then partitioning it. A statistical analysis has been performed to show the effectiveness of the proposed algorithms. In particular, three different indexes of quality, namely completeness, fairness, and robustness, have been studied.
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Title: Coverage Problem in Wireless Sensor Network: A Survey

Section 1: INTRODUCTION
Description 1: Write about the advances in wireless communication and MEMS, the importance and applications of WSNs, the resource constraints of sensor nodes, and the focus of the paper on the coverage problem in WSN.

Section 2: DESIGN CRITERIONS
Description 2: Discuss the design criteria that affect the coverage performance of WSN including deployment strategy, sensing model, sensing area, communication ranges, algorithm characteristics, sensor mobility, and other factors.

Section 3: THE RELATED PROBLEM
Description 3: Explain how coverage problems have been formulated in other fields such as the Art Gallery Problem, Circle Covering Problem, and Robotic Systems Coverage and their relevance to WSN.

Section 4: CLASSIFYING COVERAGE SCHEMES
Description 4: Classify coverage schemes into three categories: area coverage, point coverage, and path coverage, and provide a summary of each type.

Section 5: SOLUTIONS TO AREA (POINT) COVERAGE
Description 5: Introduce various protocols and algorithms designed for evaluating and improving the coverage performance of area and point coverage in WSNs, including CCP, ASCENT, OGDC, KCCS, RIS, CDCS, LDAS, LEACH, and others.

Section 6: PATH COVERAGE
Description 6: Discuss methodologies for penetration coverage in WSN and introduce algorithms to compute penetration paths (e.g., minimal exposure paths, k-barrier coverage).

Section 7: MOBILE SENSOR
Description 7: Cover the advantages of mobile sensor nodes for improving network coverage, strategies for node movement and relocation to optimize coverage, and various approaches for implementing mobility in WSNs.

Section 8: OPEN PROBLEMS
Description 8: Highlight unresolved issues in WSN coverage research including irregularity of sensing ranges, the need for accurate location information, challenges of 3D network coverage, and the integration of coverage schemes with other network properties.

Section 9: CONCLUSIONS AND FUTURE DIRECTIONS
Description 9: Summarize the survey, discuss the significance of the covered topics, and propose future research directions for coverage problems in WSN.