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

Abstract

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.