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For many envisioned applications of wireless sensor networks (WSNs), the information processing involves dealing with distributed data in the context of accurate signal detection and energy-efficient routing, which have been active research topics for many years, respectively. In this paper, we relate these two aspects via joint optimization. Considering the scenario of using distributed radar-like sensors to detect the presence of an object through active sensing, we formulate the problem of energy- efficient routing for signal detection under the Neyman-Pearson criterion, apparently for the first time. The joint optimization of detection and routing is carried out in a fusion center which precomputes the routes as a function of the geographic location to be monitored. Accordingly, we propose three different routing metrics that aim at an appropriate tradeoff between the detection performance and the energy expenditure. In particular, each metric relates the detection performance explicitly in terms of probabilities of detection and false alarm, with the energy consumed in sensing and routing. The routing problems are formulated as combinatorial optimization programs, and we provide solutions drawing on operations research. We present extensive simulation results that demonstrate the energy and detection performance tradeoffs for each proposed routing metric.