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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.

Abstract-An ad-hoc network of wireless static nodes is considered as it arises in a rapidly deployed, sensor based, monitoring system. Information is generated in certain nodes and needs to reach a set of designated gateway nodes. Each node may adjust its power within a certain range that determines the set of possible one hop away neighbors. Traffic forwarding through multiple hops is employed when the intended destination is not within immediate reach. The nodes have limited initial amounts of energy that is consumed in different rates depending on the power level and the intended receiver. We propose algorithms to select the routes and the corresponding power levels such that the time until the batteries of the nodes drain-out is maximized. The algorithms are local and amenable to distributed implementation. When there is a single power level, the problem is reduced to a maximum flow problem with node capacities and the algorithms converge to the optimal solution. When there are multiple power levels then the achievable lifetime is close to the optimal (that is computed by linear programming) most of the time. It turns out that in order to maximize the lifetime, the traffic should be routed such that the energy consumption is balanced among the nodes in proportion to their energy reserves, instead of routing to minimize the absolute consumed power.

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