Abstract
Connected plane graphs enable many local algorithmic solutions for data communication, task coordination and network maintenance in wireless sensor networks, sensor-actuator networks and distributed robotics. We study construction of such graphs by removing edges from a given network graph. We assume redundancy and coexistence, a graph structure which holds in realistic wireless network models with high probability and which assures that a connected plane graph can always be constructed with local edge removal rules. We present a local algorithm to construct such a connected plane graph. We prove algorithm correctness under redundancy and coexistence assumption. Furthermore, we discuss how far redundancy and coexistence could be weakened while still assuring correctness of the algorithm.
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