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As a burgeoning technique for signal processing, Compressed Sensing (CS) is being increasingly applied to wireless communications. However, little work is done to apply CS to multi-hop networking scenarios. In this paper, the authors investigate the application of CS to data collection in wireless sensor networks, and they aim at minimizing the network energy consumption through joint routing and compressed aggregation. They first characterize the optimal solution to this optimization problem, and then they prove its NP-completeness. They further propose a mixed-integer programming formulation along with a greedy heuristic, from which both the optimal (for small scale problems) and the near-optimal (for large scale problems) aggregation trees are obtained.
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