Minimizing transmit power consumption in multi-level WSNs for environmental monitoring

In this paper, we present two approximation algorithms for minimizing power consumption of wireless sensor networks (WSNs) in environmental monitoring applications. Most approximation algorithms for similar problems assume that the cost function satisfies the triangle inequality. For a cost function defined based on power consumption for reliable transmission between two nodes in a WSN, this assumption is not true. We first prove that we have the triangle inequality in a relaxed sense for these cost functions and then we use this in performance analysis of our two algorithms. The first algorithm is a natural bottom-up algorithm, while the second algorithm is a more complicated, top-down algorithm. We show that the solutions from both these algorithms are within a constant factor of the optimum value, and that the top-down algorithm has a better constant ratio. Our experimental results show that these two algorithms usually perform much better than proven approximation guarantees.