Wireless sensor networks generate a vast amount of data. This data, however, must be sparingly extracted to conserve energy, usually the most precious resource in battery-powered sensors. When approximation is acceptable, a model-driven approach to query processing is effective in saving energy by avoiding contacting nodes whose values can be predicted or are unlikely to be in the result set. To optimize queries such as top-k, however, reasoning directly with models of joint probability distributions can be prohibitively expensive. Instead of using models explicitly, we propose to use samples of past sensor readings. Not only are such samples simple to maintain, but they are also computationally efficient to use in query optimization. With these samples, we can formulate the problem of optimizing approximate top-k queries under an energy constraint as a linear program. We demonstrate the power and flexibility of our sampling-based approach by developing a series of top-k query planning algorithms with linear programming, which are capable of efficiently producing plans with better performance and novel features. We show that our approach is both theoretically sound and practically effective on simulated and real-world datasets. © 2006 IEEE.