Models and algorithms for energy efficient wireless sensor networks

Wireless Sensor Networks (WSNs) is an area of active research in industry and academia. WSNs can be used in a wide array of applications such as, battlefield surveillance, aerospace exploration, environmental monitoring, products tracking and supply chain management, homeland security applications, and so on. In this dissertation, we study algorithms that address two challenges faced by WSNs in applications: the need to operate distributedly and to take into account uncertain conditions. We first work on constructing efficient distributed routing algorithms for maximal data extraction problem, the second part of this thesis focuses on the effect of considering uncertain conditions for routing in WSN. The last part of the thesis introduces methodologies that address uncertainty to achieve secure localization in hostile environments. We develop efficient distributed routing algorithms for data extraction by using the Lagrangian relaxation method and the sub-gradient projection method on a maximal data extraction formulation of the routing problem. We show through computational experiments that, for the problem considered, both centralized and distributed versions of the algorithm arrive at routing solutions that are on average better than 10% from optimal after only a few iterations. We use robust optimization to address distance uncertainty in WSN routing. We develop models that incorporate uncertainty for three important problems in WSN operations: Maximum data extraction, Minimum energy consumption, and Maximum network lifetime problems. Our computational experiments show that as the uncertainty increases a robust solution for these problems provides a significant improvement in worst case performance at the expense of a small loss in optimality when compared to the optimal solution of a fixed scenario. Finally, we consider the robust analysis in secure localization for energy limited wireless sensor networks under malicious attackers in hostile environments. We present three methods: Minimum Mean Square Error (MMSE), Robust Optimization (RO) and Minimizing Minimum Mean Square Error (MMMSE) to make the estimated location attack-tolerant. Simulations show that the robust method obtains accurate location estimates in the presences of an unknown number of tampered distance data and large uncertainty set.