Efficient graph planarization in sensor networks and local routing algorithm

In this paper, we propose an efficient planarization algorithm and a routing algorithm dedicated to Unit Disk Graphs whose nodes are localized using the Virtual Raw Anchor Coordinate system (VRAC). Our first algorithm computes a planar 2-spanner under light constraints on the edge lengths and induces a total exchange of at most 6n node identifiers. Its total computational complexity is O(n Delta), with Delta the maximum degree of the communication graph. The second algorithm that we present is a simple and efficient algorithm to route messages in this planar graph that requires routing tables with only three entries. We support these theoretical results by simulations showing the robustness of our algorithms when the coordinates are inaccurate.