Construction of Generalized Ricci Flow Based Virtual Coordinates for Wireless Sensors Network

Geographic routing algorithms are well-suited to the special characteristics of WSNs. However, the performance of geographic routing is impacted by physical voids and localization errors. In this paper, we use conformal mapping and Möbius transformation to compute a new embedding of the sensor nodes in the plane such that greedy forwarding with the virtual coordinates guarantees delivery. In particular, we perform generalized Ricci flow to a planar triangulation from the sensor network topology with non-triangular faces as holes such that all the non-triangular faces are mapped to perfect circles. The generalized Ricci flow is more flexible, more robust and conformal for meshes with low quality triangulations. The generalized method allows the two circles to either intersect or separate from each other. This greatly improves the flexibility and robustness of the method. In addition, we transform the planar triangulation with perfect circles into a circular domain D in that the probability of obtuse triangles is greatly decreased. Thus greedy forwarding will never get stuck at an intermediate node. Simulation results are presented for these scenarios.