We present a distributed topology control protocol that runs on a d-QUDG for d ≥ 1/ √ 2, and computes a sparse, constant-spanner, both in Euclidean distance and in hop distance. QUDGs (short for Quasi Unit Disk Graphs) generalize Unit Disk Graphs and permit more realistic modeling of wireless networks, allowing for imperfect and non-uniform transmission ranges as well as uncertain node location information. Our protocol is local and runs in O(1) rounds. The output topology permits memoryless (geographic) routing with guaranteed delivery. In fact, when our topology control protocol is used as preprocessing step for the geographic routing protocol GOAFR+ , we get the routing time guarantee of O( 2 ) for any source-destination pair that are units away from each other in the input d-QUDG. The key idea is simple: to obtain planarity, we replace each edge intersection with a virtual node and have a real node serve as a proxy for the virtual node. This idea is supported by other parts of ...
Kevin M. Lillis, Sriram V. Pemmaraju, Imran A. Pir