Efficient data gathering using Compressed Sparse Functions

Data gathering is one of the core algorithmic and theoretic problems in wireless sensor networks. In this paper, we propose a novel approach - Compressed Sparse Functions - to efficiently gather data through the use of highly sophisticated Compressive Sensing techniques. The idea of CSF is to gather a compressed version of a satisfying function (containing all the data) under a suitable function base, and to finally recover the original data. We show through theoretical analysis that our scheme significantly outperforms state-of-the-art methods in terms of efficiency, while matching them in terms of accuracy. For example, in a binary tree-structured network of n nodes, our solution reduces the number of packets from the best-known O(kn log n) to O(k log² n), where k is a parameter depending on the correlation of the underlying sensor data. Finally, we provide simulations showing that our solution can save up to 80% of communication overhead in a 100-node network. Extensive simulations further show that our solution is robust, high-capacity and low-delay.