A wireless network consisting of a large number of small sensors with low-power transceivers can be an effective tool for gathering data in a variety of environments. The data collected by each sensor is communicated through the network to a single processing center that uses all reported data to determine characteristics of the environment or detect an event. The communication or message passing process must be designed to conserve the limited energy resources of the sensors. Clustering sensors into groups, so that sensors communicate information only to clusterheads and then the clusterheads communicate the aggregated information to the processing center, may save energy. In this paper, we propose a distributed, randomized clustering algorithm to organize the sensors in a wireless sensor network into clusters. We then extend this algorithm to generate a hierarchy of clusterheads and observe that the energy savings increase with the number of levels in the hierarchy. Results in stochastic geometry are used to derive solutions for the values of parameters of our algorithm that minimize the total energy spent in the network when all sensors report data through the clusterheads to the processing center.

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