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 and consider the cases where the link quality is not perfect. We show that these problems are NP-complete and propose
$O(1)$
-approximation algorithms for each of them. Simulations show that the proposed algorithms have good performance in terms of energy cost.