Monitoring data streams in a distributed system is the focus 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 communication overhead using naive, centralized algorithms.We present a novel geometric approach which reduces monitoring the value of a function (visa-vis a threshold) to a set of constraints applied locally on each of the streams. The constraints are used to locally filter out data increments that do not affect the monitoring outcome, thus avoiding unnecessary 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. ACM Reference Format:Sharfman, I., Schuster, A., and Keren, D. 2007. A geometric approach to monitoring threshold functions over distributed data streams.

Monitoring data streams in a distributed system is the focus 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 communication overhead using naive, centralized algorithms.We present a novel geometric approach by which an arbitrary global monitoring task can be split into a set of constraints applied locally on each of the streams. The constraints are used to locally filter out data increments that do not affect the monitoring outcome, thus avoiding unnecessary 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.

A fundamental problem in distributed computation is the distributed evaluation of functions. The goal is to determine the value of a function over a set of distributed inputs, in a communication efficient manner. Specifically, we assume that each node holds a time varying input vector, and we are interested in determining, at any given time, whether the value of an arbitrary function on the average of these vectors crosses a predetermined threshold.In this paper, we introduce a new method for monitoring distributed data, which we term shape sensitive geometric monitoring. It is based on a geometric interpretation of the problem, which enables to define local constraints on the data received at the nodes. It is guaranteed that as long as none of these constraints has been violated, the value of the function does not cross the threshold. We generalize previous work on geometric monitoring, and solve two problems which seriously hampered its performance: as opposed to the constraints used so far, which depend only on the current values of the local input vectors, here we incorporate their temporal behavior into the constraints. Also, the new constraints are tailored to the geometric properties of the specific function which is being monitored, while the previous constraints were generic.Experimental results on real world data reveal that using the new geometric constraints reduces communication by up to three orders of magnitude in comparison to existing approaches, and considerably narrows the gap between existing results and a newly defined lower bound on the communication complexity.

A fundamental problem in distributed computation is the distributed evaluation of functions. The goal is to determine the value of a function over a set of distributed inputs, in a communication efficient manner. Specifically, we assume that each node holds a time varying input vector, and we are interested in determining, at any given time, whether the value of an arbitrary function on the average of these vectors crosses a predetermined threshold.In this paper, we introduce a new method for monitoring distributed data, which we term shape sensitive geometric monitoring. It is based on a geometric interpretation of the problem, which enables to define local constraints on the data received at the nodes. It is guaranteed that as long as none of these constraints has been violated, the value of the function does not cross the threshold. We generalize previous work on geometric monitoring, and solve two problems which seriously hampered its performance: as opposed to the constraints used so far, which depend only on the current values of the local input vectors, here we incorporate their temporal behavior into the constraints. Also, the new constraints are tailored to the geometric properties of the specific function which is being monitored, while the previous constraints were generic.Experimental results on real world data reveal that using the new geometric constraints reduces communication by up to three orders of magnitude in comparison to existing approaches, and considerably narrows the gap between existing results and a newly defined lower bound on the communication complexity.

The goal of Complex Event Processing (CEP) systems is to efficiently detect complex patterns over a stream of primitive events. A pattern of particular significance is a sequence, where we are interested in identifying that a number of primitive events have arrived on the stream in a predefined order. Many popular CEP systems employ Non-deterministic Finite Automata (NFA) arranged in a chain topology to detect such sequences. Existing NFA-based mechanisms incrementally extend previously observed prefixes of a sequence until a match is found. Consequently, each newly arriving event needs to be processed to determine whether a new prefix is to be initiated or an existing one extended. This approach may be very inefficient when events at the beginning of the sequence are very frequent.We address the problem by introducing a lazy evaluation mechanism that is able to process events in descending order of selectivity. We employ this mechanism in a chain topology NFA, which waits until the most selective event in the sequence arrives and then adds events to partial matches according to a predetermined order of selectivity. In addition, we propose a tree topology NFA that does not require the selectivity order to be defined in advance. Finally, we experimentally evaluate our mechanism on real-world stock trading data, demonstrating a performance gain of two orders of magnitude, with significantly reduced memory resource requirements.