Computing and communicating functions over sensor networks

In wireless sensor networks, one is not interested in downloading all the data from all the sensors. Rather, one is only interested in collecting from a sink node a relevant function of the sensor measurements. This paper studies the maximum rate at which functions of sensor measurements can be computed and communicated to the sink node. It focuses on symmetric functions, where only the data from a sensor is important, not its identity. The results include the following. The maximum rate of downloading the frequency histogram in a random planar multihop network with n nodes is O(1/logn) A subclass of functions, called type-sensitive functions, is maximally difficult to compute. In a collocated network, they can be computed at rate O(1/n), and in a random planar multihop network at rate O(1/logn). This class includes the mean, mode, median, etc. Another subclass of functions, called type-threshold functions, is exponentially easier to compute. In a collocated network they can be computed at rate O(1/logn), and in a random planar multihop network at rate O(1/loglogn). This class includes the max, min, range, etc. The results also show the architecture for processing information across sensor networks.