1. 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. The planar
topologies constructed by current location-free methods often have large stretch factor. In this
work, we present a fine-grained and location-free network planarization method under ρ-quasi-
UDG communication model with ρ ≥ 1/ √ 2. Compared with existing location-free planarization
approaches, our method can extract a provably connected planar graph, called topological planar
simplification (TPS), from the connectivity graph in a fine-grained manner using local
connectivity information. We evaluate our design through extensive simulations and compare
with the state-of-the art approaches. The simulation results show that our method produces high-
quality planar graphs with a small stretch factor in practical large-scale networks.
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