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In this work we present new in-network techniques for communication efficient approximate query processing in wireless sensor nets. We use a model-based approach that constructs and maintains a spanning tree within the network, rooted at the base station. The tree maintains compressed summary information for each link that is used to ldquostub outrdquo traversal during query processing. Our work is based on a formal model of the in-network tree construction task framed as an optimization problem.We demonstrate hardness results for that problem, and develop efficient approximation algorithms for subtasks that are too expensive to compute exactly. We also propose efficient heuristics to accommodate a wider set of workloads, and empirically evaluate their performance and sensitivity to model changes.