Fine-Grained Location-Free Planarization in Wireless Sensor Networks

Extracting planar graph from network topologies is of great importance for efficient protocol design in wireless ad hoc and sensor networks. Previous techniques of planar topology extraction are often based on ideal assumptions, such as UDG communication model and accurate node location measurements. To make these protocols work effectively in practice, we need extract a planar topology in a location-free and distributed manner with small stretch factor. Current location-free methods cannot provide any guarantee on the stretch factor of the constructed planar topologies. In this work, we present a fine-grained and location-free network planarization method. Compared with existing location-free planarization approaches, our method can extract a high-quality planar graph, called TPS (Topological Planar Simplification), from the communication graph using local connectivity information. TPS is proved to be a planar graph and has a constant stretch factor for a large class of network instances. We evaluate our design through extensive simulations and compare with the state-of-the-art approaches. The simulation results show that our method produces planar graphs with a small constant stretch factor, often less than 1.5.