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We study the problem of constructing a data gathering tree over a wireless sensor network in order to minimize the total energy for compressing and transporting information from a set of source nodes to the sink. This problem is crucial for advanced computation-intensive applications, where traditional "maximum" in-network compression may result in significant computation energy. We investigate a tunable data compression technique that enables effective tradeoffs between the computation and communication costs. We derive the optimal compression strategy for a given data gathering tree and then investigate the performance of different tree structures for networks deployed on a grid topology as well as general graphs. Our analytical results pertaining to the grid topology and simulation results pertaining to the general graphs indicate that the performance of a simple greedy approximation to the Minimal Steiner Tree (MST) provides a constantfactor approximation for the grid topology and good average performance on the general graphs. Although theoretically, a more complicated randomized algorithm offers a poly-logarithmic performance bound, the simple greedy approximation of MST is attractive for practical implementation.

B. Krishnamachari, V. K. Prasanna and Y. Yu, "Data Gathering with Tunable Compression in Sensor Networks," in IEEE Transactions on Parallel & Distributed Systems, vol. 19, no. , pp. 276-287, 2007.
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