This paper studies the interaction between the communication costs in a sensor network and the structure of the data that it measures. We formulate an optimization problem for power efficient data gathering and show that the problem is NP-complete. We propose scalable, distributed and efficient heuristics for solving this problem and show by numerical simulations that the power consumption can be significantly improved over direct transmission or the shortest path tree. Our algorithms provide

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... lutions close to a computationally heavy heuristic used as benchmark, simulated annealing, which is provably optimal in the limit.