In-network computation in wireless sensor networks

Wireless sensor networks are networks of devices which collaborate to perform distributed sensing, processing, and possibly even actuation tasks. This thesis is a study of distributed tasks which require in-network communication and processing.; First, we study how distributed computation can be efficiently carried out over wireless networks. We formulate the problem as one of determining the optimal rate or frequency at which symmetric functions of data distributed throughout the network can be computed at a collection center. Under a deterministic framework and packet collision-based model, we derive scaling laws with respect to network size which characterize the maximum achievable computational throughput for different subclasses of symmetric functions over connectivity graphs of different topologies. The results indicate that the maximum rate can be exponentially higher in a multihop network in comparison to a single hop network, due to the ability to compress data in-network. There is also an exponential increase in the maximum computational throughput for type-sensitive functions in comparison to type-threshold functions, which are subclasses of symmetric functions that include most statistical functions of interest.; Next, we study another important metric in sensor networks, which is network lifetime. We consider a formulation of maximizing network lifetime given the simple task of downloading different quantities of data over nodes with different energy levels. We reduce the problem of choosing lifetime optimal routes to a linear program, and derive closed form solutions for some simple regular network topologies. In the final part of the thesis, we consider the problem of clock synchronization over multihop networks, which is a specific instance of a network task requiring distributed computation. We analyze a clock synchronization approach which leads to a distributed vector estimation problem based on noisy estimates of clock differences of pairs of nodes which can directly exchange packets. We establish connections between the error variance of optimal least-squares clock synchronization and resistances in electrical networks. We propose and analyze the convergence time of a distributed iterative algorithm to compute the optimal estimates. We also propose ways of exploiting the network connectivity graph structure in order to speed up computation.