This paper studies the construction of powerefficient data gathering tree for wireless ad hoc networks. Because of their high communication cost and limited capacity, a fundamental requirement in such networks is designing energy efficient data-gathering algorithms to ensure long network survivability. Two possible models for the data gathering problem are explored: scheduling model and the energy model. In the scheduling model the goal is to minimize the makespan of the most congested node, while in the energy model the goal is to maximize the lifetime of the network. We present a number of provable approximation algorithms and show inapproximation bounds for various versions of data-gathering problem.