One for All and All for One: Simultaneous Approximation of Multiple Functions over Distributed Streams.

Distributed monitoring methods address the difficult problem of continuously approximating functions over distributed streams, while minimizing the communication cost. However, existing methods are concerned with the approximation of a single function at a time. Employing these methods to track multiple functions will multiply the communication volume, thus eliminating their advantage in the first place. We introduce a novel approach that can be applied to multiple functions. Our method applies a communication reduction scheme to the set of functions, rather than to each function independently, keeping a low communication volume. Evaluation on several real-world datasets shows that our method can track many functions with reduced communication, in most cases incurring only a negligible increase in communication over distributed approximation of a single function.