Wireless sensor networks are used for structure monitoring and border surveillance. Typical applications, such as sensors embedded in the outer surface of a pipeline or mounted along the supporting structure of a bridge, feature a linear sensor arrangement. Economical power use of sensor nodes is essential for long-lasting operation. In this paper, we present MERR (Minimum Energy Relay Routing), a novel approach to energy-efficient data routing to a single control center in a linear sensor topology. Based on an optimal transmission distance, relay paths are established that aim for minimizing the total power consumption. We study MERR by both stochastic analysis and simulation, comparing it to other possible approaches and a theoretically optimal protocol. We find that MERR consumes 80% less power than conventional approaches and performs close to the theoretical optimum for practicable sensor networks.