Minimum Power Range Assignment for Symmetric Connectivity in Sensor   Networks with two Power Levels
  This paper examines the problem of assigning a transmission power to every node of a wireless sensor network. The goal is to minimize the total power consumption while ensuring that the resulting communication graph is connected. We focus on a restricted version of this Range Assignment (RA) problem in which there are two different power levels. We only consider symmetrical transmission links to allow easy integration with low level wireless protocols that typically require bidirectional communication between two neighboring nodes. We introduce a parameterized polynomial time approximation algorithm with a performance ratio arbitrarily close to $\pi^2/6$. Additionally, we give an almost linear time approximation algorithm with a tight quality bound of $7/4$. 
Stefan Hoffmann and Egon Wanke
cs.DS