Localization from mere connectivity
Proceedings of the 4th ACM international symposium on Mobile ad hoc networking & computing
Competitive online routing in geometric graphs
Theoretical Computer Science - Special issue: Online algorithms in memoriam, Steve Seiden
Wireless localization using self-organizing maps
Proceedings of the 6th international conference on Information processing in sensor networks
Network sketching or: "How Much Geometry Hides in Connectivity?--Part II"
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Localization applying an efficient neural network mapping
Proceedings of the 1st international conference on Autonomic computing and communication systems
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
On triangulations of a set of points in the plane
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
Fine-grained boundary recognition in wireless ad hoc and sensor networks by topological methods
Proceedings of the tenth ACM international symposium on Mobile ad hoc networking and computing
Greedy routing with guaranteed delivery using Ricci flows
IPSN '09 Proceedings of the 2009 International Conference on Information Processing in Sensor Networks
Covering space for in-network sensor data storage
Proceedings of the 9th ACM/IEEE International Conference on Information Processing in Sensor Networks
Resilient routing for sensor networks using hyperbolic embedding of universal covering space
INFOCOM'10 Proceedings of the 29th conference on Information communications
Localized Algorithm for Precise Boundary Detection in 3D Wireless Networks
ICDCS '10 Proceedings of the 2010 IEEE 30th International Conference on Distributed Computing Systems
IEEE Transactions on Information Theory
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A wireless sensor network can be represented by a graph. While the network graph is extremely useful, it often exhibits undesired irregularity. Therefore, special treatment of the graph is required by a variety of network algorithms and protocols. In particular, many geometry-oriented algorithms depend on a type of subgraph called Delaunay triangulation. However, when location information is unavailable, it is nontrivial to achieve Delaunay triangulation by using connectivity information only. The only connectivity-based algorithm available for Delaunay triangulation is built upon the property that the dual graph for a Voronoi diagram is a Delaunay triangulation. This approach, however, often fails in practical wireless sensor networks because the boundaries of Voronoi cells can be arbitrarily short in discrete sensor network settings. In a sensor network with connectivity information only, it is fundamentally unattainable to correctly judge neighboring cells when a Voronoi cell boundary is less than one hop. Consequently, the Voronoi diagram-based Delaunay triangulation fails. The proposed algorithm employs a distributed approach to perform centroidal Voronoi tessellation, and constructs its dual graph to yield Delaunay triangulation. It exhibits several distinctive properties. First, it eliminates the problem due to short cell boundaries and thus effectively avoids crossing edges. Second, the proposed algorithm is proven to converge and succeed in constructing a Delaunay triangulation, if the CVT cell size is greater than a constant threshold. Third, the established Delaunay triangulation consists of close-to-equilateral triangles, benefiting a range of applications such as geometric routing, localization, coverage, segmentation, and data storage and processing. Extensive simulations are carried out under various 2D network models to evaluate the effectiveness and efficiency of the proposed CVT-based triangulation algorithm.