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3DNet |
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Abstract Although most wireless terrestrial networks are based on two-dimensional (2D) design, in reality, such networks operate in three-dimensions (3D). Since most often the size (i.e., the length and the width) of such terrestrial networks is significantly larger than the differences in the third dimension (i.e., the height) of the nodes, the 2D assumption is somewhat justified and usually it does not lead to major inaccuracies. However, in some environments, this is not the case; the underwater, atmospheric, or space communications being such apparent examples. 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 project, 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 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 placements strategies is the same, this number is 43.25% higher than the number of nodes required by 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 as an important basis for extending the processes of 2D network design to 3D networks. Code polyhedra.tar.gz contains the source code, binary executable, glut32.dll and glu32.dll . To run the executable file, glut32.dll and glu32.dll must be in your path or in the folder that contains the executable. Few Screenshots of the Program |
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Publication S. M. Nazrul Alam and Zygmunt Haas, “Coverage and Connectivity in Three-Dimensional Networks”, In Proceedings of ACM MobiCom, 2006. |
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Coverage and Connectivity in Three-Dimensional Networks |
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Abstract Coverage and connectivity issues of three-dimensional (3D) networks are addressed in [2], but that work assumes that a node can be placed at any arbitrary location. In this work, we drop that assumption and rather assume that nodes are uniformly and densely deployed in a 3D space. We want to devise a mechanism that keeps some nodes active and puts other nodes into sleep so that the number of active nodes at a time is minimized (and thus network life time is maximized), while maintaining full coverage and connectivity. One simple way to do that is to partition the 3D space into cells, and only one node in each cell remains active at a time. Our results show that the number of active nodes can be minimized if the shape of each cell is a truncated octahedron. It requires the sensing range to be at least 0.542326 times the transmission radius. This value is 0.5, 0.53452 and 0.5 for cube, hexagonal prism, and rhombic dodecahedron, respectively. However, at a time the number of active nodes for cube, hexagonal prism and rhombic dodecahedron model is respectively 2.372239, 1.82615 and 1.49468 times of that of truncated octahedron model. So clearly truncated octahedron model has the highest network lifetime. We also provide a distributed topology control algorithm that can be used by each sensor node to determine its cell id using a constant number of local arithmetic operations provided that the sensor node knows its location. We also validate our results by simulation. |
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Topology Control and Network Lifetime in Three-Dimensional Wireless Sensor Networks |
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Publication S. M. Nazrul Alam and Zygmunt Haas, “Topology Control and Network Lifetime in Three-Dimensional Wireless Sensor Networks”, CORR cs.NI/0609047, 2006. |
