Abstract—Wireless sensor networks need very efficient network protocols due to the sensors’ limited communication and computation capabilities. Network planarization – finding a planar subgraph of the network that contains all the nodes – has been a very important technique for many network protocols. It first became the foundation of various well known routing protocols, including GPSR, GOAFR and several other protocols. Since then, it has also been used in numerous other applications, including data-centric storage, network localization, topology discovery, etc. However, an important problem remains: network planarization itself is very difficult. So far, efficient planarization algorithms exist only for very restrictive models: the network must be a unit-disk graph, and accurate measurements related to the node locations (e.g., node positions or angles between adjacent links) need to be known. For more practical network models, where the transmission ranges are usually ...