Machine learning has become a prominent technique used in wireless sensor networks (WSNs) in the past 10-15 years. Because of their high accuracy, adaptability, and potential to lesson computational overhead compared to existing mathematical algorithms, machine learning techniques are excellent for dynamic environments. Within machine learning, there are many different techniques to consider, such as supervised learning, unsupervised learning, reinforcement learning, and others. This paper will focus on Q-learning, and its advantages in WSN selection algorithms. We propose a Q-learning-based sensor selection framework to optimize node scheduling while providing k-coverage by learning policies that balance coverage and remaining energy. In particular, sleep scheduling algorithms are investigated and the Q-learning developed policy is compared with an existing mathematical algorithm via simulations. To conclude, the advantages and disadvantages of machine learning with resource constrained WSNs is discussed.

Achieving k-coverage in a three-dimensional field of interest is more complex compared to two-dimensional fields due to the additional spatial dimension. This paper introduces a fully decentralized algorithm to achieve energy-efficient k-coverage based on non-cooperative game theory. Sensors play the role of independent players that make a binary decision or strategy to stay ACTIVE or ASLEEP in a k cover game. Their decision will be driven by their utility to the overall network that is influenced by the reward of providing coverage to an under-covered area, or the penalty or costs of staying active and being redundant. The algorithm was tested in a simulated Python environment in comparison with a probabilistic algorithm. k-coverage was achieved with the game theory algorithm, achieving scheduling that allowed extended network lifetime than a probabilistic algorithm.

Wireless Sensor Networks (WSNs) are critical for applications requiring accurate environmental monitoring and dependable performance. A major challenge in these networks is the occurrence of coverage holes—unmonitored regions that degrade reliability and efficiency. This paper presents a geometry-driven hole detection framework in which sensors are modeled as uniform disks, overlapping areas are merged to form a unified coverage region, and the convex hull is computed to define the network boundary. Subtracting the coverage region from the hull exposes genuine coverage gaps. To restore coverage, we propose an energy-aware Quality-of-Service (QoS) scheduler that prioritizes hole healing according to sensor battery levels and hole criticality, thereby extending network lifetime. Two complementary algorithms are introduced: a lattice-based sensor placement strategy that ensures minimum 1-coverage and a priority scheduling mechanism that determines the order of hole restoration. Simulation results demonstrate that the proposed framework achieves high precision in hole detection, reduces the number of sensors required for recovery, and significantly improves energy efficiency, ultimately enhancing both reliability and performance in WSNs.

This paper focuses on the problem of connected$k$-coverage in PWSNs, where every point in a planar field of interest (PFoI) is sensed by at least$k$sensors$(k>1)$simultaneously, while all the underlying sensors of the network are mutually connected either directly or indirectly. In order to solve this problem, we develop a global framework using an irregular hexagonal tessellation, considering stochastic sensing models for the sensors. In our study, we propose an irregular hexagon, denoted by$IrHx(r_{s}/n)$, for tessellating a PFoI and deploying the sensors with the goal to achieve connected$k$-coverage, where$n>1$is a natural number and$r_{s}$is the radius of the sensing range of the sensor. First, we tessellate a PFoI with adjacent and congruent regular hexagonal tiles. Then, we modify the properties of this regular hexagonal tile so as to construct our irregular hexagonal tile,$\operatorname{IrHx}(r s / n)$, and generate a guided tessellation utilizing the existing regular hexagonal tessellation. Second, we compute the optimal value$\boldsymbol{n}^{\boldsymbol{*}}$for generating optimal$\mathbf{Ir} {H x}(\boldsymbol{r} \boldsymbol{s} \boldsymbol{n} \boldsymbol{)}$-based tessellation. Third, we determine the value of stochastic sensing radius$r_{s}{ }^{*}$, and using this$\operatorname{IrHx}\left(\boldsymbol{r}_{s} \boldsymbol{*}^{*} / \boldsymbol{n}^{*}\right)$-based tessellation configuration, we compute the minimum sensor density, which is required for stochastic$k$-coverage in PWSNs. This helps us compute the minimum number of sensors to$k$-cover a PFoI, while accounting for stochastic sensing model. Next, we establish the necessary relationship for ensuring network connectivity in$k$-covered PWSNs. Finally, we propose our sensor scheduling protocol for stochastic$k$-coverage, and substantiate our theoretical analysis with simulation results.

Wireless Sensor Networks (WSNs) play a critical role in environmental monitoring, surveillance, and battlefield communications. There has been an increasing demand for WSNs that optimize network lifetime and energy consumption, a critical design challenge. Previous research has made use of two separate optimization paths: global deployment geometry to reduce communication costs to transmit to the Base Station (BS), or optimization of local network topology to improve routing efficiency. In this paper, we introduce the Optimal Rhombic Cylindrical Hybrid Intelligent Deployment (ORCHID) protocol that will synergize the two optimization paths. ORCHID operates by considering tessellation within a geometrically optimized cylinder. This structure enables an intelligent protocol architecture, featuring a deterministic, energy-aware cluster head selection process that replaces probabilistic mechanisms found in other protocols. We will compare the performance of this protocol to a previously proposed cylindrical LEACH implementation. Through simulations, ORCHID shows improvements in network lifetime, cumulative throughput, and energy consumption. The protocol has very low overhead, which will be scaled along with performance to compare to the most recent similar protocols such as PEG-GA-VC(3) (2019), a Hybrid k-means clustering algorithm (2017), and LEACH3D (2015).

Coverage and connectivity are the major performance metrics that reflect the quality of service provided by heterogeneous planar wireless sensor networks (PWSNs) monitoring a planar field of interest (PFoI), where the deployed sensors may not necessarily have the same capabilities in terms of their sensing range, communication range, and maximum battery-power capacity. Precisely, coverage is considered as the main functionality of PWSNs, which is meaningful only when connectivity is guaranteed. Therefore, it is important that both coverage and connectivity be jointly considered in the deployment of heterogeneous PWSNs. In order to account for joint coverage and connectivity, we propose to solve the problem of connected k -coverage in heterogeneous PWSNs, where every point in a PFoI is covered by at least k sensors simultaneously, while all the deployed sensors are mutually connected, either directly or indirectly, with k > 1. While most existing studies of this problem focus on homogeneous sensors, which have the same above-mentioned capabilities (i.e., initial energy, sensing range, and communication range), our study in this article considers heterogeneous ones. More specifically, we propose a hierarchical (or multitier) deployment of heterogeneous sensors in a square FoI, which is divided into concentric square bands with the same width difference to achieve k -coverage of this PFoI. Based on this multitier sensor deployment and the slicing of a square FoI into square bands for k -coverage, we establish the necessary relationship for connectivity among the sensors located in adjacent bands. Finally, we propose our heterogeneous k -coverage protocol and validate our theoretical analysis using simulation results. We find that the deployment of heterogeneous sensors helps achieve much better results compared to those obtained using homogeneous sensors. Furthermore, our proposed protocol outperforms an existing connected k -coverage protocol for heterogeneous PWSNs with respect to various performance metrics.

In this paper, we focus on the problem of connected k-coverage in planar wireless sensor networks (PWSNs), where every point in a field of interest (FoI) is covered by at least$k$sensors simultaneously, while all the participating sensors are mutually connected, where k > 1. To this end, we develop a global framework using a square tessellation that considers both deterministic and stochastic sensing models. Initially, we tessellate a planar FoI into adjacent and congruent square tiles. In each tile of this tessellation, we construct a cusp-square area for sensor placement to achieve k-coverage. Based on this cusp-squared square tile configuration, we compute the minimum sensor density that is required for deterministic and stochastic k-coverage in PWSNs. Then, we establish the necessary relationship that should exist between the sensing and communication ranges of the sensors to maintain network connectivity in k-covered PWSNs. Finally, we propose our stochastic k-coverage protocol for sensor scheduling and substantiate our theoretical analysis with simulation results.

The problem of coverage is one of the most crucial issues among the problems in the lifecycle of the development of wireless sensor networks (WSNs). It is still open and stirs as much concern in the research community in this area. The problem of k -coverage in WSNs is even more challenging. In this article, we investigate the k -coverage problem in planar (or two-dimensional) WSNs, where each point in a field of interest (FoI) is covered by at least k sensors simultaneously, where k ≥ 1. Our contribution is four-fold: First, we determine the optimal planar convex tile that maximizes the usage of the sensors’ sensing range. Then, we propose a few sensor placement strategies based on the degree of coverage k using a hexagonal tiling-based approach. In addition, we compute the sensor density (i.e., number of sensors per unit area) for each of the above sensor placement strategies. Second, we propose a generalized one using irregular hexagons, which are denoted by IRH(r/n) , where r stands for the radius of the sensors’ sensing range and n ≥ 2 is a natural number. Also, we derive the corresponding sensor density. Moreover, we prove that IRH(r/n) are capable of tiling the Euclidean plane using a mathematical induction proof. Third, we compute the relationship between the sensing range r of the sensors and their communication range R for the above sensor placement strategies. Fourth, we corroborate our analysis with simulation results.

Physical security is essential to safeguarding critical areas. Here, we focus on the physical security problem in three-dimensional (3D) stealthy lattice wireless sensor networks using a 3D sensor belt around a critical space. Specifically, we propose a theoretical framework to investigate the 3D k-barrier coverage problem, where any path crossing this belt intersects with the sensing range of at least k sensors. Precisely, we study this problem from a tiling viewpoint, where the sensing ranges of the sensors are touching (or kissing) each other. We analyze various 3D deterministic sensor deployment methods yielding simple cubic, body centered cubic, face centered cubic, and hexagonal close-packed lattice wireless sensor networks. First, using the concept of the unit cell covered volume ratio, we prove that none of these 3D lattices guarantee k-barrier coverage. Second, to remedy this problem, we consider the great rhombicuboctahedron (GR), a polyhedral space-filler. We introduce the concept of intruder’s abstract paths along a 3D k-barrier covered belt, and compute their number. Also, we propose a polynomial representation for all abstract paths. In addition, we compute the number of sensors deployed over a 3D k-barrier covered belt using GR. Third, we corroborate our analysis with numerical and simulation results.

Coverage is an essential task in the design of wireless sensor networks. We noticed that the problem of coverage in a two-dimensional (2D) space has similarity with the 2D tiling problem, which can be stated as follows: How can a 2D space be tiled by replicas of a set (or tiles)? This is a 2D instance of the second part of Hilbert's 18th problem: Is there a polyhedron that admits an anisohedral tiling only in three dimensions, i.e., tiles a 3D space, but does not admit an isohedral tiling? In this paper, we investigate the problem of 2D k-coverage, where each point in a 2D field is covered by at least k sensors, k≥1. In our study, we found that it is helpful to identify a 2D convex tile that best approximates the sensors' sensing range. First, we propose some sensor placement strategies using a hexagonal tiling-based method, and compute the corresponding sensor density. Second, we suggest a more general one using irregular hexagon, denoted by IRH(r/n), where r stands for the radius of the sensors' sensing range, and n≥2. We show that IRH(r/n) is a 2D tile, and derive the corresponding minimum sensor density. Third, we compute the relationship between the sensors' communication range R and r for each placement strategy. We corroborate our analysis with simulation results.

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.

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.

The Twelfth Annual International Conference on Distributed Computing in Sensor Systems (DCOSS) will be held in Washington DC, USA on May 26-28, 2016. This conference broadly focuses on the design, development, and optimization of large scale networked sensor systems. In addition to the established tracks in the previous editions of DCOSS, such as Algorithms and Performance Analysis, Applications, Systems, Real Deployments and Tools, Signal Processing and Information Theory, this twelfth edition includes a new Track of the Year, called "Cloud Computing and Applications to Sensing Systems." DCOSS 2016 includes a high-quality technical program consisting of keynotes, research papers, Poster and Demo session, and Ph.D. Forum. This year we received 65 submissions in response to the call for papers. Each paper was reviewed by at least three experts in the field. After detailed on-line discussions with the Track Chairs, 24 papers were finally accepted, leading to an acceptance ratio of 37%. Specifically, the program covers important aspects of distributed computing in sensor systems, such as mobile crowdsourcing, energy efficiency and communication, routing, tracking and localization, security, and applications and outdoor testbed, to name a few. Additionally, there is one workshop that addresses challenging research topics in sensor networking. We believe the technical program will provide an exciting forum for researchers and practitioners to exchange cutting-edge ideas in distributed sensor systems.

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 -cov erage and com posite geographic for warding in 3D duty-cycled WSNs, called 3D- k Cov-ComFor . We found a close-to-perfect match between our theoretical and simulation results.

In immobile wireless sensor networks with constant data reporting, the sensors nearer the sink are responsible for forwarding data to it on behalf of all other sensors in the network. Those sensors suffer from a severe batter power depletion problem, also known as the energy sink-hole problem. In this paper, we study the above problem in duty-cycled connected${\mbi{k}}$-covered wireless sensor networks, where each point in a field of interest is covered by at least${\mbi{k}}$sensor. In order to change the neighbors of a sink over time, our solutions suggest the use of mobile proxy sinks that collect data from source sensors and drop them off at an immobile sink. Our proposed three-tier architecture has immobile source sensors, immobile sinks, and mobile proxy sinks. First, we present our fundamental results for the design of duty-cycled connected${\mbi{k}}$-covered wireless sensor networks. Second, we provide the first formal analysis of the performance of joint mobility and routing in this type of network. Precisely, we investigate the best mobility strategy of mobile proxy sinks to minimize the total energy consumption for data collection. Third, we propose joint mobility and routing schemes based on the number of immobile sinks and mobile proxy sinks. We provide a thorough analytical model for our schemes. Finally, we evaluate their performance by simulation. Our results show their significant improvement of the network lifetime compared to a solution without mobile proxy sinks.

Coverage is one of the fundamental concepts in the design of wireless sensor networks (WSNs) in the sense that the monitoring quality of a phenomenon depends on the quality of service provided by the sensors in terms of how well a field of interest is covered. It enables the sensors to detect any event that may occur in the field, thus, meeting the application-specific requirements. Several applications require k - coverage , where each point in the field is covered by at least k sensors, which helps increase data availability to ensure better data reliability. Achieving k -coverage of a field of interest becomes a more challenging issue in sparsely deployed WSNs. Though the problem of coverage in WSNs has been well studied in the literature, only little research efforts have been devoted to the case of sparsely deployed WSNs. Thus, in this article, we investigate the problem of k -coverage in sparse WSNs using static and mobile sensors, which do not necessarily have the same communication range, sensing range, and energy supply. Precisely, we propose an optimized, generalized framework for k -coverage in sparsely deployed WSNs, called k -SCHEMES, which exploits sensor heterogeneity and mobility. First, we characterize k -coverage using heterogeneous sensors based on Helly 's Theorem. Second, we introduce our energy-efficient four-tier architecture to achieve mobile k -coverage of a region of interest in a field. Third, on top of this architecture, we suggest two data-gathering protocols, called direct data-gathering and forwarding chain-based data-gathering, using the concept of mobile proxy sink. We found that the second data-gathering protocol outperforms the first one. For energy-efficient forwarding, we compute the minimum transmission distance between any pair of consecutive mobile proxy sinks forming the forwarding chain as well as the corresponding optimum number of mobile proxy sinks in this chain. We corroborate our analysis with several simulation results.

Sensing coverage is an essential functionality of wireless sensor networks (WSNs). However, it is also well known that coverage alone in WSNs is not sufficient, and hence network connectivity should also be considered for the correct operation of WSNs. In this paper, we address the problem of k-coverage in WSNs such that in each scheduling round, every location in a monitored field (or simply field) is covered by at least k active sensors while all active sensors are being connected. Precisely, we study sensors duty-cycling strategies for generating k-coverage configurations in WSNs. First, we model the k-coverage problem in WSNs. Second, we derive a sufficient condition of the sensor spatial density for complete k-coverage of a field. We also provide a relationship between the communication and sensing ranges of sensors to maintain both k-coverage of a field and connectivity among all active sensors. Third, we propose four configuration protocols to solve the problem of k-coverage in WSNs. We prove that our protocols select a minimum number of sensors to achieve full k-coverage of a field while guaranteeing connectivity between them. Then, we relax some widely used assumptions for coverage configuration in WSNs, to promote the use of our proposed protocols in real-world sensing applications. Our simulation results show that our protocols outperform an existing distributed k-coverage configuration protocol.

It is well known that sensor duty-cycling is an important mechanism that helps densely deployed wireless sensor networks (WSNs) save energy. On the other hand, geographic forwarding is an efficient scheme for WSNs as it requires maintaining only local topology information to forward data to their destination. Most of geographic forwarding protocols assume that all sensors are always on (or active) during forwarding. However, such an assumption is unrealistic for real-world applications where sensors are switched on or off (or inactive). In this paper, we describe our cover-sense-inform (CSI) framework for k-covered WSNs, where each point in a sensor field is covered by at least k active sensors. In CSI, k-coverage, sensor scheduling, and data forwarding are jointly considered. Based on our previous work on connected k-coverage [3], we propose the first design of geographic forwarding protocols for duty-cycled k-covered WSNs with and without data aggregation. Then, we evaluate the performance of our joint k-coverage and geographic forwarding protocols and compare them to CCP [37], a k-Coverage Configuration Protocol, with a geographic forwarding protocol on top of it, such as BVGF [36], which we have slightly updated in such a way that it considers energy for a fair comparison. Simulation results show that our joint protocols outperform CCP+BVGF.

In a wireless sensor network (WSN), connectivity enables the sensors to communicate with each other, while sensing coverage reflects the quality of surveillance. Although the majority of studies on coverage and connectivity in WSNs consider 2D space, 3D settings represent more accurately the network design for real-world applications. As an example, underwater sensor networks require design in 3D rather than 2D space. In this paper, we focus on the connectivity and k-coverage issues in 3D WSNs, where each point is covered by at least k sensors (the maximum value of k is called the coverage degree). Precisely, we propose the Reuleaux tetrahedron model to characterize k-coverage of a 3D field and investigate the corresponding minimum sensor spatial density. We prove that a 3D field is guaranteed to be k-covered if any Reuleaux tetrahedron region of the field contains at least k sensors. We also compute the connectivity of 3D k-covered WSNs. Based on the concepts of conditional connectivity and forbidden faulty sensor set, which cannot include all the neighbors of a sensor, we prove that 3D k-covered WSNs can sustain a large number of sensor failures. Precisely, we prove that 3D k-covered WSNs have connectivity higher than their coverage degree k. Then, we relax some widely used assumptions in coverage and connectivity in WSNs, such as sensor homogeneity and unit sensing and communication model, so as to promote the practicality of our results in real-world scenarios. Also, we propose a placement strategy of sensors to achieve full k-coverage of a 3D field. This strategy can be used in the design of energy-efficient scheduling protocols for 3D k-covered WSNs to extend the network lifetime.

Coverage is an essential task in sensor deployment for the design of wireless sensor networks. While most existing studies on coverage consider homogeneous sensors, the deployment of heterogeneous sensors represents more accurately the network design for real-world applications. In this paper, we focus on the problem of connected k-coverage in heterogeneous wireless sensor networks. Precisely, we distinguish two deployment strategies, where heterogeneous sensors are either randomly or pseudo-randomly distributed in a field. While the first deployment approach considers a single layer of heterogeneous sensors, the second one proposes a multi-tier architecture of heterogeneous sensors to better address the problems introduced by pure randomness and heterogeneity.

Most of geographic forwarding protocols assume that all sensors are always on. Such an assumption is unrealistic for applications where sensors are switched on or off. This paper focuses on k-covered wireless sensor networks (WSNs), where each point in a field is covered by at least k sensors. First, we characterize k-coverage. Then, we propose an energy-efficient scheduling protocol for k-covered WSNs. Third, we propose the first design of a geographic forwarding protocol for duty-cycled k-covered WSNs with data aggregation. Finally, we evaluate the performance of our joint k-coverage and geographic forwarding protocol and compare it to the Coverage Configuration Protocol (CCP) with BVGF on top of it. Simulation results show that our joint protocol outperforms the resulting protocol, CCP+BVGF.

Sensing coverage reflects the quality of surveillance of a field by a wireless sensor network (WSN). This paper investigates the problem of minimum connected k-coverage in WSNs, where each point in a field is covered (or sensed) by at least k active sensors while minimizing the necessary total number of active sensors and ensuring connectivity between them. In this paper, we propose two k-coverage protocols using different scheduling approaches. In the first protocol, called self-scheduling driven k-coverage (SSCk), each sensor turns itself on based on the local information it has about its sensing neighbors in order to k-cover its sensing range. The second protocol, called triggered-scheduling driven k-coverage (TSCk), allows a sensor to trigger a necessary number of its sensing neighbors to become active in order to achieve k-coverage of its sensing range. Then, we relax some commonly used assumptions for coverage configuration protocols in WSNs to promote the use of SSCkand TSCkin realworld sensing applications. Simulation results show that TSCkoutperforms SSCkwith regard to the number of sensors required for connected k-coverage as well as the network lifetime. We find that SSCkoutperforms an existing connected k-coverage protocol for WSNs.

Connectivity , primarily a graph-theoretic concept, helps define the fault tolerance of wireless sensor networks (WSNs) in the sense that it enables the sensors to communicate with each other so their sensed data can reach the sink. On the other hand, sensing coverage , an intrinsic architectural feature of WSNs plays an important role in meeting application-specific requirements, for example, to reliably extract relevant data about a sensed field. Sensing coverage and network connectivity are not quite orthogonal concepts. In fact, it has been proven that connectivity strongly depends on coverage and hence considerable attention has been paid to establish tighter connection between them although only loose lower bound on network connectivity of WSNs is known. In this article, we investigate connectivity based on the degree of sensing coverage by studying k-covered WSNs, where every location in the field is simultaneously covered (or sensed) by at least k sensors (property known as k-coverage , where k is the degree of coverage ). We observe that to derive network connectivity of k -covered WSNs, it is necessary to compute the sensor spatial density required to guarantee k -coverage. More precisely, we propose to use a model, called the Reuleaux Triangle , to characterize k -coverage with the help of Helly's Theorem and the analysis of the intersection of sensing disks of k sensors. Using a deterministic approach, we show that the sensor spatial density to guarantee k -coverage of a convex field is proportional to k and inversely proportional to the sensing range of the sensors. We also prove that network connectivity of k -covered WSNs is higher than their sensing coverage k . Furthermore, we propose a new measure of fault tolerance for k -covered WSNs, called conditional fault tolerance , based on the concepts of conditional connectivity and forbidden faulty sensor set that includes all the neighbors of a given sensor. We prove that k -covered WSNs can sustain a large number of sensor failures provided that the faulty sensor set does not include a forbidden faulty sensor set.

Although most of the studies on coverage and connectivity in wireless sensor networks (WSNs) considered two-dimensional (2D) settings, such networks can in reality be accurately modeled in a three-dimensional (3D) space. The concepts of continuum percolation theory best fit the problem of connectivity in WSNs to find out whether the network provides long-distance multihop communication. In this paper, we focus on percolation in coverage and connectivity in 3D WSNs. We say that the network exhibits a coverage percolation (respectively, connectivity percolation) when a giant covered region (respectively, giant connected component) almost surely spans the entire network for the first time. Because of the dependency between coverage and connectivity, the problem is not only a continuum percolation problem but also an integrated continuum percolation problem. Thus, we propose an integrated-concentric-sphere model to address coverage and connectivity in 3D WSNs in an integrated way. First, we compute the critical density lambdaCconabove which coverage percolation in 3D WSNs will almost surely occur. Second, we compute the critical density lambdacconabove which connectivity percolation in 3D WSNs will almost surely occur. Third, we compute the critical density lambdaccov-conabove which both coverage and connectivity percolation in 3D WSNs will almost surely occur. For each of these three problems, we also compute their corresponding critical network degree. Our results can be helpful in the design of energy-efficient topology control protocols for 3D WSNs in terms of coverage and connectivity.

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.

While sensing coverage reflects the surveillance quality provided by a wireless sensor network (WSN), network connectivity enables data gathered by sensors to reach a central node, called the sink. Given an initially uncovered field and as more and more sensors are continuously added to a WSN, 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 as the sensing-coverage phase transition (SCPT). Also, given an originally disconnected WSN and as more and more sensors are added, the number of connected components changes such that the WSN suddenly becomes connected at some point. We call this sudden change as the network-connectivity phase transition (NCPT). The nature of such phase transitions is a central topic in percolation theory of Boolean models. In this paper, we propose a probabilistic approach to compute the covered area fraction at critical percolation for both of the SCPT and NCPT problems. Because sensing coverage and network connectivity are not totally orthogonal, we also propose a model for percolation in WSNs, called correlated disk model, which provides a basis for solving the SCPT and NCPT problems together.

Static always-on wireless sensor networks (WSNs) are affected by the energy sink-hole problem, where sensors nearer a central gathering node, called the sink, suffer from significant depletion of their battery power (or energy). It has been shown through analysis and simulation that it is impossible to guarantee uniform energy depletion of all the sensors in static uniformly distributed always-on WSNs with constant data reporting to the sink when the sensors use their nominal communication range to transmit data to the sink. We prove that the energy sink-hole problem can be solved provided that the sensors adjust their communication ranges. This solution, however, imposes a severe restriction on the size of a sensor field. To overcome this limitation, we propose a sensor deployment strategy based on energy heterogeneity with a goal that all the sensors deplete their energy at the same time. Simulation results show that such a deployment strategy helps achieve this goal. To solve the energy sink-hole problem for homogeneous WSNs, we propose a localized energy-aware-Voronoi-diagram-based data forwarding (EVEN) protocol. EVEN combines sink mobility with a new concept, called energy-aware Voronoi diagram. Through simulations, we show that EVEN outperforms similar greedy geographical data forwarding protocols and has performance that is comparable to that of an existing data collection protocol that uses a joint mobility and routing strategy. Precisely, we find that EVEN yields an improvement of more than 430 percent in terms of network lifetime.

Traditional connectivity is a graph-theoretic concept that has been widely used as a measure of the fault tolerance in wireless sensor networks. The classical connectivity, however, assumes that any subset of nodes can potentially fail at the same time, including the entire neighbor set of any node. In this paper, we propose a new measure of fault tolerance, called conditional fault-tolerance, for a class of wireless sensor networks, named k-covered wireless sensor networks (kcwsn), using the concept of forbidden faulty set. Our forbidden faulty set analysis of conditional fault-tolerance prohibits having a simultaneous failure of all the neighbors of any node. We characterize kcwsn with either homogeneous or non-homogeneous sensors based on the assumptions of random uniform distribution of the sensors and circular model of their transmission and sensing ranges. In particular, we compute the minimum node degree of kcwsn. We also prove that in general, the relationship between transmission and sensing ranges (R≥2r) does not always imply network connectivity even if sensing coverage is guaranteed. Moreover, we propose two conditional fault-tolerance measures for kcwsn: one based on the concept of conditional connectivity, the other using a new concept that is called conditional coverage. Our results prove that kcwsn can sustain a large number of sensor failures provided that the faulty set does not include the forbidden faulty set.

Uncertainty is an inherent characteristic of wireless sensor networks (WSNs) due to uncertainty in wireless communication links, limited resources (e.g., energy, storage, CPU, bandwidth), mobility and topology, to name a few. Thus, resource-efficient data dissemination between source sensors and a sink becomes a challenging task, particularly if the sink is moving in a wireless sensor field. This paper proposes an energy-aware protocol, called weighted entropy data dissemination (WEDAS) for disseminating data to the mobile sink in WSNs using an information theoretic approach. The proposed protocol attempts to quantify the uncertainty of position of a mobile sink and the remaining energy uncertainty of static sensors in order to select the most appropriate ones that will act as data disseminators between static sources and the mobile sink. The WEDAS protocol favors sensor nodes whose weighted entropy with respect to their location and remaining energy is the minimum to participate in building dissemination paths between sources and the mobile sink. Specifically, we introduce the concepts of relative mobility zone of a sink, which includes its most probable future positions, and coordinator node set, which restricts the search space of candidate data disseminators, to conduct the selection process. The analytic results show that the selection of sensors with minimum weighted entropy as data disseminators depends on not only their remaining energy but also their relative positions with respect to the mobile sink, which meets our goals of extending the lifetime of WSNs by minimizing and balancing energy utilization of sensor nodes.

Wireless sensor networks (WSNs) consist of large numbers of unattended sensors with limited storage, energy (battery power) and computational and communication capabilities. Because battery power is the most crucial resource for sensor nodes and delay time is a critical metric for certain WSN applications that require fast response time, data dissemination between source sensors and sinks, which is an essential activity in WSNs, should be done in an energy efficient and timely manner. In this paper, we characterize the trade-off between energy savings and source-to-sink delay in order to extend the operation of individual sensors and hence increase the lifetime of the WSN, and enable sinks to receive sensed data in a timely fashion and make appropriate decisions quickly. To this end, the proposed data dissemination protocol decomposes the transmission range of sensors into a certain number of concentric circular bands (CCBs) based on a minimal distance between consecutive forwarding sensors. Then, it provides a classification of these CCBs based on their exterior radii which will help a source sensor express its degree of interest (DoI) in minimizing two metrics, namely energy consumption and source-to-sink delay. We prove that the use of sensors nodes, which lie on or closely to the shortest path between a source and the sink, as proxy forwarders, helps minimize these two metrics. Our numerical results show that the second CCB minimizes energy consumption; the last CCB minimizes source-to-sink delay; and the middle CCBs trade off between the two metrics in disseminating the monitored data towards the sink.

A mobile ad hoc network (MANET) is a set of mobile nodes that agreed upon forming a temporary, spontaneous network in spite of the lack of any infrastructure or centralized administration. MANET topology changes frequently and arbitrarily due to node mobility. Therefore, an efficient routing protocol is required to cope with the dynamic change of MANET topology, which requires discovering and maintaining new routes, in this paper we propose a route discovery protocol based on location information, which could be provided to MANET nodes by a Global Positioning System (GPS). Our route discovery protocol utilizes the essential features of Voronoi diagrams in order to reduce the search space of routes by allowing only a small subset of MANET nodes, called authorized forwarders, to forward a route request. This results in a restrictive, selective route discovery protocol, which significantly reduces the routing overhead compared to other location-based routing protocol, such as LAR.

Summary form only given. Mobile ad hoc networks (MANET) and the Internet exhibit differences in their network architecture. These differences concern the various sorts of assumptions imposed not only on the structure and topology of the underlying networks, but also on communication patterns of mobile nodes in both networks. Integrating MANET and the Internet into a hybrid network is a challenging problem due to these differences. We propose a three-layer approach that uses both mobile IP and dynamic destination-sequenced distance vector (DSDV) to integrate these two types of networks into a hybrid environment, in order to provide MANET nodes with Internet connectivity and access to the Internet resources. Our approach is based on the use of mobile gateways as an interface between MANET and the Internet. These mobile gateways can use mobile IP when they communicate with the Internet and DSDV when they interact with MANET. We also show the results of several simulation experiments that were conducted to study the integrated environment.

To combine the advantages of mobile ad hoc networks (MANETs) and the Internet, we propose an approach that will integrate them into a hybrid, unified network enabling MANET nodes to have Internet connectivity regardless of their location in MANET. In order to best benefit MANET from Internet resources access, we introduce mobile gateways, which are moving around the boundary of fixed Internet gateways' coverage range, to act as an interface between MANET and the Internet. Mobile gateways are designed in a way to overcome the network architectural mismatches that exist between MANET and the Internet and widen the coverage range affixed Internet gateways. More specifically, mobile gateways are equipped with two interfaces allowing them to communicate simultaneously with MANET and the Internet using an ad hoc routing protocol and Mobile IP, respectively. Our experiments, which were conducted using the network simulator ns2, adopted Mobile IP protocol and dynamic source distance vector (DSDV) routing protocol, and showed that density and mobility of gateways as well as time-to-live of agent advertisements have an impact on the performance of the hybrid network.

The quality of service (QoS) of wireless Internet access that could be provided to multihop wireless networks, so-called mobile ad hoc networks (MANETs), is highly dependent on the quality of the design of the intermediate facility that will integrate MANET and the Internet. This facility is equipped with a hybrid mechanism being able to fulfill the working requirements of MANET and the Internet so that it can connect to either one of these orthogonal network architectures. The architecture that we propose in order to provide MANET nodes with Internet access utilizes fixed gateways (or access points) and exploits the mobility capability of additional mobile ones. Since Internet access to MANET nodes is provided through mobile gateways, the quality of such service depends on the selection procedure used by MANET nodes to choose the most convenient mobile gateways and register with. In this paper, we suggest to use a hybrid criterion based on the weighted sum of the Euclidean distance between MANET nodes and mobile gateways, and the load of mobile gateways, defined as the number of MANET nodes currently registered with them. Moreover, the sum of the weights is normalized to one, where each weight measures the level of interest of the corresponding criterion in the hybrid one. Simulation results show that the hybrid criterion has an impact on the quality of wireless Internet access service depending on the level of interest assigned to each of the Euclidean distance and load criteria in the weighted sum.

This paper discusses how a program can be represented by a binary relation, R, and how to decompose the latter into a set of rectangular relations. Next, we present our methodology based on relational operators and dependence relations, to show how we can use these rectangles to obtain more interesting ones that describe the entire behavior of every variable in the program. The notion of lattice of maximal rectangles is effective in that it permits to have a particular representation of the program which shows all the different parts that constitute the original program. By looking at this lattice structure, we find that the set of the leaves of this lattice, which represent "pertinent" rectangles associated to output variables, gives a minimal program covering.