We address the problem of finding optimal strategies for computing Boolean symmetric functions. We consider a collocated network, where each node's transmissions can be heard by every other node. Each node has a Boolean measurement and we wish to compute a given Boolean function of these measurements with zero error. We allow for block computation to enhance data fusion efficiency, and determine the minimum worst-case total bits to be communicated to perform the desired computation. We restrict attention to the class of symmetric Boolean functions, which only depend on the number of 1s among the n measurements. We define three classes of functions, namely threshold functions, delta functions and interval functions. We provide exactly optimal strategies for the first two classes, and an order-optimal strategy with optimal preconstant for interval functions. Using these results, we can characterize the complexity of computing percentile type functions, which is of great interest. In our analysis, we use lower bounds from communication complexity theory, and provide an achievable scheme using information theoretic tools.
We consider the problem of data harvesting in wireless sensor networks. A designated collector node seeks to compute a function of the sensor measurements. For a directed graph G = (V ,ℰ) on the sensor nodes, we wish to determine the optimal encoders on each edge which achieve zero-error block computation of the function at the collector node. Our goal is to characterize the rate region in R∣ℰ∣.