On the Construction of Data Aggregation Tree with Minimum Energy Cost in   Wireless Sensor Networks: NP-Completeness and Approximation Algorithms
  In many applications, it is a basic operation for the sink to periodically collect reports from all sensors. Since the data gathering process usually proceeds for many rounds, it is important to collect these data efficiently, that is, to reduce the energy cost of data transmission. Under such applications, a tree is usually adopted as the routing structure to save the computation costs for maintaining the routing tables of sensors. In this paper, we work on the problem of constructing a data aggregation tree that minimizes the total energy cost of data transmission in a wireless sensor network. In addition, we also address such a problem in the wireless sensor network where relay nodes exist. We show these two problems are NP-complete, and propose O(1)-approximation algorithms for each of them. Simulations show that the proposed algorithms each have good performance in terms of the energy cost. 
Tung-Wei Kuo, Kate Ching-Ju Lin, Ming-Jer Tsai
cs.NI