Minimum-Power Routing in Wireless Ad Hoc Networks

One of the major concerns in ad hoc wireless networks is reducing node energy consumption. For the purpose of energy conservation, each node can (possibly dynamically) adjust its transmitting power, based on the distance to the receiving node and the background noise. In the most common power-attenuation model [10], the signal power falls as 1 dκ where d is the Euclidean distance from the transmitter antenna and κ is the pass-loss exponent of the wireless environment–a real constant typically between 2 and 5. Assume that all nodes have the same power threshold for signal detection, which is typically normalized to one. Then, the power required to cover a transmission range of radius d is dκ. To simplify the problem, we assume that all nodes have the same maximum transmission range R. We use V to denote the set of nodes, and G = (V,E, c) be the weighted graph such that for any pair of nodes u and v, uv ∈ E if and only if ‖uv‖ ≤ R, and the weight of an edge uv is c (uv) = ‖uv‖. We assume that the graph G is connected. We use − → G to denote the weighted directed graph which is directed version of G.