Abstract: Topology control is an important energy-saving technique used in wireless sensor networks. It has evolved into two dominant research directions,power control and sleep scheduling. Based on the observation of existing problems,this paper did fundamental research on topology control. We made a full-scale consideration on energy consumption of the network, both consumed in communications and in idle states. Then, under an ideal circumstance, we proposed a clear definition of the topology control problem with the objective to minimize energy consumption. We proved that it is NP-hard, and informally discussed the computational complexity of more realistic topology control problems. Based on that, we further put forward three necessary principles about how to design energy efficient topology control protocols.It is wished that this paper could contribute to the development of better topology control protocols.

Key words: Sensor networks, Topology control, Energy efficiency, Complexity, Design principles