We consider the problem of adjusting the transmit powers of nodes in a multihop wireless network (also called an ad hoc network) to create a desired topology. We formulate it as a constrained optimization problem with two constraints-connectivity and biconnectivity, and one optimization objective-maximum power used. We present two centralized algorithms for use in static networks, and prove their optimality. For mobile networks, we present two distributed heuristics that adaptively adjust node transmit powers in response to topological changes and attempt to maintain a connected topology using minimum power. We analyze the throughput, delay, and power consumption of our algorithms using a prototype software implementation, an emulation of a power-controllable radio, and a detailed channel model. Our results show that the performance of multihop wireless networks in practice can be substantially increased with topology control.
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