Construction of Optimal Data Aggregation Trees for Wireless Sensor Networks

This paper considers the problem of constructing data gathering trees in a wireless sensor network for a group of sensor nodes to send collected information to a single sink node. Sensors form application-directed groups and the sink node communicates with the group members, called source nodes, to gather the desired data using a multicast tree rooted at the sink node. The data gathering tree contains the sink node, all the source nodes, and some other non-source nodes. Our goal of constructing such a data gathering tree is to minimize the number of non-source nodes to be included in the tree so as to save energies of as many non-source nodes as possible. It can be shown that the optimization problem is NP-hard. We first propose an approximation algorithm with a performance ratio of four, and then give a distributed algorithm corresponding to the approximation algorithm. Extensive simulations are performed to study the performance of the proposed algorithm. The results show that the proposed algorithm can find a tree of a good approximation to the optimal tree and has a high degree of scalability.