A distance-based scheme for reducing bandwidth in distributed geometric monitoring

Tracking the value of a function computed from a dynamic, distributed data stream is a challenging problem with many real-world applications. Continuously forwarding data updates can be costly, yet complex functions are difficult to evaluate when data is not centralized. One general approach to continuous distributed monitoring is the Geometric Monitoring (GM) family of techniques. GM reduces the functional monitoring problem to a set of local constraints that each node checks locally, and uses a simple protocol to update those constraints as needed.While most work on GM focuses on reducing the number of messages exchanged by the common GM protocol, with one recent notable exception, there has been little attention to reducing the size of those messages, which impacts bandwidth.We propose the Distance Scheme: a novel bandwidth-efficient variation of the GM protocol that reduces the size of most monitoring messages in GM to a single scalar, and is compatible with the large body of prior work on GM. We apply it to monitor three different functions using three real-world datasets, and show it substantially reduces bandwidth while requiring fewer messages to be transmitted than the current state-of-the-art approach. We further describe a value-based scheme that, while typically outperformed by the Distance Scheme, is simpler to apply, matches state-of-the-art bandwidth performance with fewer messages, and is also compatible with existing work.