Efficient Summing over Sliding Windows

This paper considers the problem of maintaining statistic aggregates over the last W elements of a data stream. First, the problem of counting the number of 1's in the last W bits of a binary stream is considered. A lower bound of {\Omega}(1/{\epsilon} + log W) memory bits for W{\epsilon}-additive approximations is derived. This is followed by an algorithm whose memory consumption is O(1/{\epsilon} + log W) bits, indicating that the algorithm is optimal and that the bound is tight. Next, the more general problem of maintaining a sum of the last W integers, each in the range of {0,1,...,R}, is addressed. The paper shows that approximating the sum within an additive error of RW{\epsilon} can also be done using {\Theta}(1/{\epsilon} + log W) bits for {\epsilon}={\Omega}(1/W). For {\epsilon}=o(1/W), we present a succinct algorithm which uses B(1 + o(1)) bits, where B={\Theta}(Wlog(1/W{\epsilon})) is the derived lower bound. We show that all lower bounds generalize to randomized algorithms as well. All algorithms process new elements and answer queries in O(1) worst-case time.Comment: A shorter version appears in SWAT 201

Continuous Monitoring of Distributed Data Streams over a Time-based Sliding Window

The past decade has witnessed many interesting algorithms for maintaining statistics over a data stream. This paper initiates a theoretical study of algorithms for monitoring distributed data streams over a time-based sliding window (which contains a variable number of items and possibly out-of-order items). The concern is how to minimize the communication between individual streams and the root, while allowing the root, at any time, to be able to report the global statistics of all streams within a given error bound. This paper presents communication-efficient algorithms for three classical statistics, namely, basic counting, frequent items and quantiles. The worst-case communication cost over a window is $O(\frac{k} {\epsilon} \log \frac{\epsilon N}{k})$ bits for basic counting and $O(\frac{k}{\epsilon} \log \frac{N}{k})$ words for the remainings, where $k$ is the number of distributed data streams, $N$ is the total number of items in the streams that arrive or expire in the window, and $\epsilon < 1$ is the desired error bound. Matching and nearly matching lower bounds are also obtained.Comment: 12 pages, to appear in the 27th International Symposium on Theoretical Aspects of Computer Science (STACS), 201

S-Store: Streaming Meets Transaction Processing

Stream processing addresses the needs of real-time applications. Transaction processing addresses the coordination and safety of short atomic computations. Heretofore, these two modes of operation existed in separate, stove-piped systems. In this work, we attempt to fuse the two computational paradigms in a single system called S-Store. In this way, S-Store can simultaneously accommodate OLTP and streaming applications. We present a simple transaction model for streams that integrates seamlessly with a traditional OLTP system. We chose to build S-Store as an extension of H-Store, an open-source, in-memory, distributed OLTP database system. By implementing S-Store in this way, we can make use of the transaction processing facilities that H-Store already supports, and we can concentrate on the additional implementation features that are needed to support streaming. Similar implementations could be done using other main-memory OLTP platforms. We show that we can actually achieve higher throughput for streaming workloads in S-Store than an equivalent deployment in H-Store alone. We also show how this can be achieved within H-Store with the addition of a modest amount of new functionality. Furthermore, we compare S-Store to two state-of-the-art streaming systems, Spark Streaming and Storm, and show how S-Store matches and sometimes exceeds their performance while providing stronger transactional guarantees

Long-term adaptation and distributed detection of local network changes

We present a statistical approach to distributed detection of local latency shifts in networked systems. For this purpose, response delay measurements are performed between neighbouring nodes via probing. The expected probe response delay on each connection is statistically modelled via parameter estimation. Adaptation to drifting delays is accounted for by the use of overlapping models, such that previous models are partially used as input to future models. Based on the symmetric Kullback-Leibler divergence metric, latency shifts can be detected by comparing the estimated parameters of the current and previous models. In order to reduce the number of detection alarms, thresholds for divergence and convergence are used. The method that we propose can be applied to many types of statistical distributions, and requires only constant memory compared to e.g., sliding window techniques and decay functions. Therefore, the method is applicable in various kinds of network equipment with limited capacity, such as sensor networks, mobile ad hoc networks etc. We have investigated the behaviour of the method for different model parameters. Further, we have tested the detection performance in network simulations, for both gradual and abrupt shifts in the probe response delay. The results indicate that over 90% of the shifts can be detected. Undetected shifts are mainly the effects of long convergence processes triggered by previous shifts. The overall performance depends on the characteristics of the shifts and the configuration of the model parameters