An Approximation Algorithm for the Maximum-Lifetime Data Aggregation Tree Problem in Wireless Sensor Networks

This paper studies the problem of constructing maximum-lifetime data aggregation trees in wireless sensor networks for collecting sensor readings. This problem is known to be NP-hard. Wireless sensor networks in which transmission power levels of sensors are adjustable and heterogeneous are considered. An approximation algorithm is developed to construct a data aggregation tree whose inverse lifetime is guaranteed to be within a bound from the optimal one. Adjustable transmission power levels of the sensors introduce an additional term in the bound compared with the bound for networks in which transmission power levels of all sensors are fixed. The additional term is proportional to the difference between the maximum and minimum amounts of energy for a sensor to transmit a message using respectively its maximum and minimum transmission power levels. The proposed algorithm is further enhanced to obtain an improved version. Simulation results show that properly adjusting transmission power levels of the sensors yields higher lifetime of the network than keeping their transmission power levels at the maximum level.