On the Connectivity of Sensor Networks Under Random Pairwise Key Predistribution

We study the secure and reliable connectivity of wireless sensor networks under the heterogeneous pairwise key predistribution scheme. This scheme was recently introduced as an extension of the random pairwise key predistribution scheme of Chan et al. to accommodate networks where the constituent sensors have different capabilities or requirements for security and connectivity. For simplicity, we consider a heterogeneous network where each of the n sensors is classified as type-1 (respectively, type-2) with probability μ (respectively, 1-μ) where 0<μ<1. Each type-1 (respectively, type-2) node selects 1 (respectively, Kn) other nodes uniformly at random to be paired with; according to the pairwise scheme each pair is then assigned a unique pairwise key so that they can securely communicate with each other. We establish critical conditions on n, μ, and Kn such that the resulting network has minimum node degree of at least k with high probability in the limit of large network size. Our result constitutes a zero-one law for the minimum node degree of the recently introduced inhomogeneous random K-out graph model. This constitutes a crucial step towards establishing a similar zero-one law for the k-connectivity of the graph; i.e., for the property that the network remains connected despite the failure of any k-1 nodes or links. We present numerical results that indicate the usefulness of our results in selecting the parameters of the scheme in practical settings with finite number of sensors.

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 lambdaC con above which coverage percolation in 3D WSNs will almost surely occur. Second, we compute the critical density lambdac con above which connectivity percolation in 3D WSNs will almost surely occur. Third, we compute the critical density lambdac cov-con above 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.

We consider secure and reliable connectivity in wireless sensor networks that utilize the heterogeneous random key predistribution scheme. We model the unreliability of wireless links by an on/off channel model that induces an Erdős-Renyi graph, while the heterogeneous scheme induces an inhomogeneous random key graph. The overall network can thus be modeled by the intersection of both graphs. We present conditions (in the form of zero-one laws) on how to scale the parameters of the intersection model, so that with high probability: i) all of its nodes are connected to at least ${k}$ other nodes, i.e., the minimum node degree of the graph is no less than $ {k}$ , and ii) the graph is $ {k}$ -connected, i.e., the graph remains connected even if any $ {k} - {1}$ nodes leave the network. These results are shown to complement and generalize several previous results in the literature. We also present numerical results to support our findings in the finite-node regime. Finally, we demonstrate via simulations that our results are also useful when the on/off channel model is replaced with the more realistic disk communication model .

We investigate k-connectivity in secure wireless sensor networks under the random pairwise key predistribution scheme with unreliable links; a network is said to be k-connected if it remains connected despite the failure of any of its (k - 1) nodes or links. With wireless communication links modeled as independent on-off channels, this amounts to analyzing a random graph model formed by intersecting a random K-out graph and an Erdös-Rényi graph. We present conditions on how to scale the parameters of this intersection model so that the resulting graph is k-connected with probability approaching to one (resp. zero) as the number of nodes gets large. The resulting zero-one law is shown to improve and sharpen the previous result on the 1-connectivity of the same model. We also provide numerical results to support our analysis and show that even in the finite node regime, our results can provide useful guidelines for designing sensor networks that are secure and reliable.

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

We investigate the secure connectivity of wireless sensor networks under the pairwise key distribution scheme of Chan et al.. Unlike recent work which was carried out under the assumption of full visibility, here we assume a (simplified) communication model where unreliable wireless links are represented as on/off channels. We present conditions on how to scale the model parameters so that the network i) has no secure node which is isolated, and ii) is securely connected, both with high probability when the number of sensor nodes becomes large. The results are given in the form of zero-one laws, and exhibit significant differences with corresponding results in the full visibility case.

In the precondition of the basic connectivity of wireless sensor networks, how to control spreading of the virus infection is the most challenging security problem in a large number of sensor nodes deployed randomly. Existing research results show that network topology is complex and spreading of virus infection heavily. In order to constitute the reasonable immune strategy and control the spreading of virus infection effectively in sensor networks. in this paper, a virus spreading model with average degree constraint was proposed. For this model, With increasing communication radius and constraining node degree, the inconsistency of network topology connectivity and sparseness can be solved. Our scheme can decrease working nodes, guarantee network topology sparseness; the effect of activity nodes-density d, spread efficiency lambda on the spreading of virus infection was studied. The theoretical analysis and analog simulation show that there is a critical value in this model based on average degree constraint, and only when the product of spread efficiency and activity nodes-density goes beyond the critical value that the virus infection can spread continuously.

Summary form only given. As the energy consumption in wireless sensor nodes is dominated by the radio transmission circuitry, the network configuration must be designed to minimize the power consumption by transmission radios. Sensor nodes are generally equipped with short-range radios that require low power consumption. But the current technology allows each node to adjust its transmission power. We consider the dual power radios in which the radio of each node can be assigned high-or low-power during the network initializing stage. Our primary goal in such an assignment is to minimize the overall power consumption by radios to maximize the network lifetime while maintaining the full network connectivity, the most fundamental network functionality. Using a graph-theoretic approach, we formulate the problem as a "minimum subgraph" problem, show its NP-completeness, establish upper and lower bounds on the optimum solution, and present a near-optimal heuristic algorithm and simulation results.

In this paper, we study the connectivity properties of a wireless sensor network from an information-theoretic viewpoint. We consider both regular linear (one-dimensional) and planar (two-dimensional) networks with unreliable sensor nodes, i.e., each node is inactive/dead with a certain probability. We study the following problems: 1) what is the fundamental limit on the data rate that such a network can support for a single sensor node to the destination under transmission power and network-topology constraints? 2) What are the constraints on the network topology such that any (single) sensor can communicate with the destination at a desired rate? For problem 1), we provide upper and lower bounds on the achievable data rate, and for problem 2), we provide upper and lower bounds on the distance between the nodes required for communication at the desired rate.

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

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

Intermediate-quality links often cause vulnerable connectivity in wireless sensor networks, but packet losses caused by such volatile links are not easy to trace. In order to equip link layer protocol designers with a reliable test and debugging tool, we develop a reactive interferer to generate packet loss patterns precisely. By using intentional interference to emulate parameterized lossy links with very low intrusiveness, our tool facilitates both robustness evaluation of protocols and flaw detection in protocol implementation.

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

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

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