A distributed delaunay triangulation algorithm based on centroidal voronoi tessellation for wireless sensor networks

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.

[1]  Yunhuai Liu,et al.  Surface Coverage in Wireless Sensor Networks , 2009, IEEE INFOCOM 2009.

[2]  Wheeler Ruml,et al.  Improved MDS-based localization , 2004, IEEE INFOCOM 2004.

[3]  Qiang Du,et al.  Centroidal Voronoi Tessellations: Applications and Algorithms , 1999, SIAM Rev..

[4]  Hongyi Wu,et al.  Optimal surface deployment problem in wireless sensor networks , 2012, 2012 Proceedings IEEE INFOCOM.

[5]  G. Giorgetti,et al.  Wireless Localization Using Self-Organizing Maps , 2007, 2007 6th International Symposium on Information Processing in Sensor Networks.

[6]  Stefan Funke,et al.  Network sketching or: "How Much Geometry Hides in Connectivity?--Part II" , 2007, SODA '07.

[7]  Yunhao Liu,et al.  Fine-grained boundary recognition in wireless ad hoc and sensor networks by topological methods , 2009, MobiHoc '09.

[8]  Errol L. Lloyd.  On triangulations of a set of points in the plane , 1977, 18th Annual Symposium on Foundations of Computer Science (sfcs 1977).

[9]  Hongyi Wu,et al.  Localized Algorithm for Precise Boundary Detection in 3D Wireless Networks , 2010, 2010 IEEE 30th International Conference on Distributed Computing Systems.

[10]  Prosenjit Bose,et al.  Competitive Online Routing in Geometric Graphs , 2004, SIROCCO.

[11]  Jie Gao,et al.  Connectivity-Based Localization of Large Scale Sensor Networks with Complex Shape , 2008, IEEE INFOCOM 2008 - The 27th Conference on Computer Communications.

[12]  Mark de Berg,et al.  Computational geometry: algorithms and applications , 1997 .

[13]  Hongyi Wu,et al.  A distributed triangulation algorithm for wireless sensor networks on 2D and 3D surface , 2011, 2011 Proceedings IEEE INFOCOM.

[14]  Roger Wattenhofer,et al.  Greedy Routing with Bounded Stretch , 2009, IEEE INFOCOM 2009.

[15]  Wei Zeng,et al.  Covering space for in-network sensor data storage , 2010, IPSN '10.

[16]  Wei Zeng,et al.  Resilient Routing for Sensor Networks Using Hyperbolic Embedding of Universal Covering Space , 2010, 2010 Proceedings IEEE INFOCOM.

[17]  Ying Zhang,et al.  Localization from mere connectivity , 2003, MobiHoc '03.

[18]  Jie Gao,et al.  Greedy routing with guaranteed delivery using Ricci flows , 2009, 2009 International Conference on Information Processing in Sensor Networks.

[19]  Donald J. Newman,et al.  The hexagon theorem , 1982, IEEE Trans. Inf. Theory.

[20]  Li Li,et al.  Localization applying an efficient neural network mapping , 2007, Autonomics.