Coverage and Connectivity in Three-Dimensional Networks

Most wireless terrestrial networks are designed based on the assumption that the nodes are deployed on a two-dimensional (2D) plane. However, this 2D assumption is not valid in underwater, atmospheric, or space communications. In fact, recent interest in underwater acoustic ad hoc and sensor networks hints at the need to understand how to design networks in 3D. Unfortunately, the design of 3D networks is surprisingly more difficult than the design of 2D networks. For example, proofs of Kelvin's conjecture and Kepler's conjecture required centuries of research to achieve breakthroughs, whereas their 2D counterparts are trivial to solve. In this paper, we consider the coverage and connectivity issues of 3D networks, where the goal is to find a node placement strategy with 100% sensing coverage of a 3D space, while minimizing the number of nodes required for surveillance. Our results indicate that the use of the Voronoi tessellation of 3D space to create truncated octahedral cells results in the best strategy. In this truncated octahedron placement strategy, the transmission range must be at least 1.7889 times the sensing range in order to maintain connectivity among nodes. If the transmission range is between 1.4142 and 1.7889 times the sensing range, then a hexagonal prism placement strategy or a rhombic dodecahedron placement strategy should be used. Although the required number of nodes in the hexagonal prism and the rhombic dodecahedron placement strategies is the same, this number is 43.25% higher than the number of nodes required by the truncated octahedron placement strategy. We verify by simulation that our placement strategies indeed guarantee ubiquitous coverage. We believe that our approach and our results presented in this paper could be used for extending the processes of 2D network design to 3D networks.Comment: To appear in ACM Mobicom 200

Connectivity-guaranteed and obstacle-adaptive deployment schemes for mobile sensor networks

Mobile sensors can relocate and self-deploy into a network. While focusing on the problems of coverage, existing deployment schemes largely over-simplify the conditions for network connectivity: they either assume that the communication range is large enough for sensors in geometric neighborhoods to obtain location information through local communication, or they assume a dense network that remains connected. In addition, an obstacle-free field or full knowledge of the field layout is often assumed. We present new schemes that are not governed by these assumptions, and thus adapt to a wider range of application scenarios. The schemes are designed to maximize sensing coverage and also guarantee connectivity for a network with arbitrary sensor communication/sensing ranges or node densities, at the cost of a small moving distance. The schemes do not need any knowledge of the field layout, which can be irregular and have obstacles/holes of arbitrary shape. Our first scheme is an enhanced form of the traditional virtual-force-based method, which we term the Connectivity-Preserved Virtual Force (CPVF) scheme. We show that the localized communication, which is the very reason for its simplicity, results in poor coverage in certain cases. We then describe a Floor-based scheme which overcomes the difficulties of CPVF and, as a result, significantly outperforms it and other state-of-the-art approaches. Throughout the paper our conclusions are corroborated by the results from extensive simulations

On the vulnerabilities of voronoi-based approaches to mobile sensor deployment

Mobile sensor networks are the most promising solution to cover an Area of Interest (AoI) in safety critical scenarios. Mobile devices can coordinate with each other according to a distributed deployment algorithm, without resorting to human supervision for device positioning and network configuration. In this paper, we focus on the vulnerabilities of the deployment algorithms based on Voronoi diagrams to coordinate mobile sensors and guide their movements. We give a geometric characterization of possible attack configurations, proving that a simple attack consisting of a barrier of few compromised sensors can severely reduce network coverage. On the basis of the above characterization, we propose two new secure deployment algorithms, named SecureVor and Secure Swap Deployment (SSD). These algorithms allow a sensor to detect compromised nodes by analyzing their movements, under different and complementary operative settings. We show that the proposed algorithms are effective in defeating a barrier attack, and both have guaranteed termination. We perform extensive simulations to study the performance of the two algorithms and compare them with the original approach. Results show that SecureVor and SSD have better robustness and flexibility and excellent coverage capabilities and deployment time, even in the presence of an attac

Push & Pull: autonomous deployment of mobile sensors for a complete coverage

Mobile sensor networks are important for several strategic applications devoted to monitoring critical areas. In such hostile scenarios, sensors cannot be deployed manually and are either sent from a safe location or dropped from an aircraft. Mobile devices permit a dynamic deployment reconfiguration that improves the coverage in terms of completeness and uniformity. In this paper we propose a distributed algorithm for the autonomous deployment of mobile sensors called Push&Pull. According to our proposal, movement decisions are made by each sensor on the basis of locally available information and do not require any prior knowledge of the operating conditions or any manual tuning of key parameters. We formally prove that, when a sufficient number of sensors are available, our approach guarantees a complete and uniform coverage. Furthermore, we demonstrate that the algorithm execution always terminates preventing movement oscillations. Numerous simulations show that our algorithm reaches a complete coverage within reasonable time with moderate energy consumption, even when the target area has irregular shapes. Performance comparisons between Push&Pull and one of the most acknowledged algorithms show how the former one can efficiently reach a more uniform and complete coverage under a wide range of working scenarios.Comment: Technical Report. This paper has been published on Wireless Networks, Springer. Animations and the complete code of the proposed algorithm are available for download at the address: http://www.dsi.uniroma1.it/~novella/mobile_sensors