Extremal properties of three-dimensional sensor networks with applications

We analyze various critical transmitting/sensing ranges for connectivity and coverage in three-dimensional sensor networks. As in other large-scale complex systems, many global parameters of sensor...

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.

We study the coverage properties of large-scale sensor networks. Three coverage measures are defined to characterize the fraction of the area covered by sensors (area coverage), the fraction of sensors that can be removed without reducing the covered area (node coverage), and the capability of the sensor network to detect objects moving in the network (detectability), respectively. We approach the coverage problem from a theoretical perspective and explore the fundamental limits of the coverage of a large-scale sensor network. We characterize the asymptotic behavior of the coverage measures for a variety of sensor network scenarios. We find that the coverage of a sensor network exhibits different behaviors for different network configuration and parameters. Based on the analytical characterizations of the network coverage, we further discuss the implications to network planning and protocol performance of sensor networks.

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.

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

The main study of traditional probability coverage problem in wireless sensor networks (WSNs) is aiming at two-dimensional space, however, most practical applications of wireless sensor network is placed in a three-dimensional sensor networks. Therefore, probability model is introduced for three-dimensional WSNs. This paper presents a method that using Voronoi divide to control the Scheduling of the probability model nodes in the target area. Also, a coverage control algorithm based on probability model (PMCCA) is proposed. We verify the effectiveness and the practice of PMCCA algorithm by comparing PMCCA algorithm to another algorithm in simulation experiment.

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.

Wireless Sensor networks have become one of the most widely-used forms of ad-hoc networks which have countless number of applications in the modern life. Due to the unreliable communication medium and the failure prone sensors, coverage is an important functional property of a sensor network. Coverage is represented as a function of sensor density, which in turn depends on sensing range and the deployment function. The sensing range and the deployment function have random nature that can greatly affect sensor coverage. In this study, we subjected a densely deployed sensor network to stochastic variations in sensing range and deployment. Also, we captured deployment variations in space dimension by a random deployment pattern and a random noise. In addition, we considered time dependent random variation in noise and environmental factors. More specifically, we studied the effect of randomness resulting in a certain percentage of uncovered area in the network.

It is our great pleasure to welcome you to the 3rd ACM Workshop on Security of Ad Hoc and Sensor Networks (SASN'05), held in conjunction with the 12th ACM Conference on Computer and Communications Security (CCS'05), November 7, 2005, in Alexandria, Virginia.This year we received a total of 39 submissions on various aspects of ad-hoc and sensor network security. The program committee selected 6 as regular papers that cover a variety of topics, including trust establishment in Mobile Ad-Hoc Networks (MANETs), security of vehicular ad-hoc networks, secure group communication, key pre-distribution for sensor networks, jamming attacks against sensor network MAC protocols, and defense against Denial-of-Service (DoS) attacks. This year we continue the tradition of SASN'03 and SASN'04 to encourage the presentation and discussion of work-in-progress on ad-hoc and sensor network security. Among the 39 submissions, the program committee selected 7 papers to present in work-in-progress sessions, covering topics on anonymous routing for MANETs, key distribution for inter-group multicast in ad-hoc networks, improved topology assumptions for threshold cryptography in MANETs, RFID security, tracing in mobile wireless sensor networks, time synchronization attacks in sensor networks, and coordinated deployment for improving secure communications and sensing coverage in wireless sensor networks. In addition, the program includes a panel on Advances in Sensor and Ad-hoc Network Security and an invited keynote talk by Radha Poovandran (University of Washington) on Information Assurance in MANETs and Wireless Sensor Networks. We hope that these proceedings will serve as a valuable reference for security researchers and developers.

We give, for the first time, a precise mathematical analysis of the connectivity and security properties of sensor networks that make use of the random pre-distribution of keys. We also show how to set the parameters - pool and key-ring size - in such a way that the network is not only connected with high probability via secure links, but also provably resilient, in the following sense: we formally show that any attacker that captures sensors at random with the aim of compromising a constant fraction of the secure links, must capture at least a constant fraction of the nodes of the network. In the context of wireless sensor networks where random pre-distribution of keys is employed, we are the first to provide a mathematically precise proof, with a clear indication of parameter choice, that two crucial properties connectivity via secure links and resilience against malicious attacks - can be obtained simultaneously. Our theoretical results are complemented by extensive simulations that reinforce our main conclusions

Contiki’s Cooja is a very popular wireless sensor network (WSN) simulator, but it lacks support for modelling sensing coverage, focusing instead on network connectivity and protocol performance. However, in practice, it is the ability of a sensor network to provide a satisfactory level of coverage that defines its ultimate utility for end-users. We introduce WSN-Maintain, a Cooja-based tool for coverage and network lifetime evaluation in an in-building WSN. To extend the network lifetime, but still maintain the required quality of coverage, the tool finds coverage redundant nodes, puts them to sleep and automatically turns them on when active nodes fail and coverage quality decreases. WSN-Maintain together with Cooja allow us to evaluate different approaches to maintain coverage. As use cases to the tool, we implement two redundant node algorithms: greedy-maintain, a centralised algorithm, and local-maintain, a localised algorithm to configure the initial network and to turn on redundant nodes. Using data from five real deployments, we show that our tool with simple redundant node algorithms and reading correlation can improve energy efficiency by putting more nodes to sleep.

For the node deployment problem in three-dimensional heterogeneous sensor networks, the traditional virtual force method is prone to local optimization and the parameters required for calculation are uncertain. A spatial deployment algorithm for 3D mobile wireless sensor networks based on weighted Voronoi diagram is proposed (TDWVADA) to solve the problem. Based on the positions and weights of all nodes in the monitoring area, a three-dimensional weighted Voronoi diagram is constructed. Next, the central position of each node’s the Voronoi region is calculated and the position is regarded as target position of the node movement. Each node moves from the original position to the target position to complete one iteration. After multiple iterations, each node is moved to the optimal deployment location and network coverage is improved. In view of the initial centralized placement of sensor nodes, the addition of virtual force factors is added to the TWDVDA algorithm. An improved algorithm TDWVADA-I was proposed. The algorithm enables nodes that are centrally placed to spread quickly and speeds up deployment. The simulation results show that TDWVADA and TDWVADA-I effectively improve the network coverage of the monitored area compared to the virtual force algorithm and the unweighted Voronoi method. Compared with the virtual force method, the coverage of TDWVADA has increased from 90.53% to 96.70%, and the coverage of TDWVADA-I has increased from 81.12% to 96.56%. Compared with the Voronoi diagram method, the coverage of TDWVADA has increased from 85.01% to 96.70%, and the coverage of TDWVADA-I has increased from 80.82% to 96.56%. TDWVADA and TDWVADA-I also greatly reduce the energy consumption of the network. Experimental results demonstrate the effectiveness of the algorithms.

Network connectivity characterises the ability to deliver data to the sensor network from a source node to a receiver node. A significant problem with these networks occurs when a sensor node fails, leading to a loss of network connectivity. In these cases, some network areas remain isolated, and therefore the nodes cannot transmit data to the central node. The paper presents and studies the characteristics of a sensor network(SN) with mesh topology, which reflects the ability of the network to establish connections between network elements within the geometric boundaries of the sensor field and the primary node (coordinator), accumulating data from all sensors in the network. The research aims to study the connectivity and reliability of sensor networks by identifying the interdependence of probabilistic energy characteristics. Well-known is the impact on these characteristics of the wireless sensor network parameters as geometric dimensions, distribution model of sensor devices in the sensor field, mesh network topology, and radio communication range.

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.

Protrusion of lamellipodia during cell migration depends on the assembly of actin network. The assembly mechanism, based on dendritic filament branching, has been investigated in reconstituted in vitro systems, but little is known about the dynamical and structural properties of the actin network in the lamellipodia of migrating cells. The length and orientation of filaments are difficult to measure directly in either optical or electron microscopy images because of the high filament density and overlapping of individual filaments. Here, we use the non-uniformity of optical images of the lamellipodia to extract information about the structural and dynamical properties of the underlying actin network. To determine the relationship between the image features and the properties of the network, we performed simulations of actin network assembly, based on the hypothesis of stochastic branching and capping of filaments, and produced computed ;fluorescence' and ;electron microscopy' images of the simulated network. By varying simulation parameters, in particular the actin filament density, length and orientation, we closely reproduced the contrast and the characteristic diagonal criss-cross pattern observed in the experimental optical images. Thus, matching the images of the simulated network to the experimental images allowed us to estimate parameters of actin filament network in lamellipodia.