In wireless ad-hoc networks, routing and power consumption are intrinsically connected since the transmit power level is adjusted depending on the location of the next hop node. Our objective is to route the traffic such that the system lifetime is maximized. In the previous works, we have formulated the problem and proposed heuristic algorithms. In this paper, fast approximate algorithms are proposed both in single commodity case and in the multicommodity case along with the analysis which enables us to control the trade-off between the performance bound and the running time. The problem is then extended to have an additional constraint on the delay.