A Geometric Approach to Monitoring Threshold Functions Over Distributed Data Streams

Monitoring data streams in a distributed system is the fo-cus of much research in recent years. Most of the proposed schemes, however, deal with monitoring simple aggregated values, such as the frequency of appearance of items in the streams. More involved challenges, such as the important task of feature selection (e.g., by monitoring the information gain of various features), still require very high communica-tion overhead using naive, centralized algorithms. We present a novel geometric approach by which an arbi-trary global monitoring task can be split into a set of con-straints applied locally on each of the streams. The con-straints are used to locally filter out data increments that do not affect the monitoring outcome, thus avoiding unnec-essary communication. As a result, our approach enables monitoring of arbitrary threshold functions over distributed data streams in an efficient manner. We present experimental results on real-world data which demonstrate that our algorithms are highly scalable, and considerably reduce communication load in comparison to centralized algorithms. 1