46,577 research outputs found

    Sliding Window Property Testing for Regular Languages

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    We study the problem of recognizing regular languages in a variant of the streaming model of computation, called the sliding window model. In this model, we are given a size of the sliding window n and a stream of symbols. At each time instant, we must decide whether the suffix of length n of the current stream ("the active window") belongs to a given regular language. Recent works [Moses Ganardi et al., 2018; Moses Ganardi et al., 2016] showed that the space complexity of an optimal deterministic sliding window algorithm for this problem is either constant, logarithmic or linear in the window size n and provided natural language theoretic characterizations of the space complexity classes. Subsequently, [Moses Ganardi et al., 2018] extended this result to randomized algorithms to show that any such algorithm admits either constant, double logarithmic, logarithmic or linear space complexity. In this work, we make an important step forward and combine the sliding window model with the property testing setting, which results in ultra-efficient algorithms for all regular languages. Informally, a sliding window property tester must accept the active window if it belongs to the language and reject it if it is far from the language. We show that for every regular language, there is a deterministic sliding window property tester that uses logarithmic space and a randomized sliding window property tester with two-sided error that uses constant space

    AFQN: approximate Qn estimation in data streams

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    We present afqn (Approximate Fast Qn), a novel algorithm for approximate computation of the Qn scale estimator in a streaming setting, in the sliding window model. It is well-known that computing the Qn estimator exactly may be too costly for some applications, and the problem is a fortiori exacerbated in the streaming setting, in which the time available to process incoming data stream items is short. In this paper we show how to efficiently and accurately approximate the Qn estimator. As an application, we show the use of afqn for fast detection of outliers in data streams. In particular, the outliers are detected in the sliding window model, with a simple check based on the Qn scale estimator. Extensive experimental results on synthetic and real datasets confirm the validity of our approach by showing up to three times faster updates per second. Our contributions are the following ones: (i) to the best of our knowledge, we present the first approximation algorithm for online computation of the Qn scale estimator in a streaming setting and in the sliding window model; (ii) we show how to take advantage of our UDDSketch algorithm for quantile estimation in order to quickly compute the Qn scale estimator; (iii) as an example of a possible application of the Qn scale estimator, we discuss how to detect outliers in an input data stream

    Fast online computation of the Qn estimator with applications to the detection of outliers in data streams

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    We present FQN (Fast Qn), a novel algorithm for online computation of the Qn scale estimator. The algorithm works in the sliding window model, cleverly computing the Qn scale estimator in the current window. We thoroughly compare our algorithm for online Qn with the state of the art competing algorithm by Nunkesser et al., and show that FQN (i) is faster, requiring only O(s) time in the worst case where s is the length of the window (ii) its computational complexity does not depend on the input distribution and (iii) it requires less space. To the best of our knowledge, our algorithm is the first that allows online computation of the Qn scale estimator in worst case time linear in the size of the window. As an example of a possible application, besides its use as a robust measure of statistical dispersion, we show how to use the Qn estimator for fast detection of outliers in data streams. Extensive experimental results on both synthetic and real datasets confirm the validity of our approach

    Coupling reduced models for optimal motion estimation

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    International audienceThe paper discusses the issue of motion estimation by image assimilation in numerical models, based on Navier-Stokes equations. In such context, models' reduction is an attractive approach that is used to decrease cost in memory and computation time. A reduced model is obtained from a Galerkin projection on a subspace, defined by its orthogonal basis. Long temporal image sequences may then be processed by a sliding-window method. On the first sub-window, a fixed basis is considered to define the reduced model. On the next ones, a Principal Order Decomposition is applied, in order to define a basis that is simultaneously small-size and adapted to the studied image data. Results are given on synthetic data and quantified according to state-of-the-art methods. Application to satellite images demonstrates the potential of the approach

    Continuous Nearest Neighbor Queries over Sliding Windows

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    Abstract—This paper studies continuous monitoring of nearest neighbor (NN) queries over sliding window streams. According to this model, data points continuously stream in the system, and they are considered valid only while they belong to a sliding window that contains 1) the W most recent arrivals (count-based) or 2) the arrivals within a fixed interval W covering the most recent time stamps (time-based). The task of the query processor is to constantly maintain the result of long-running NN queries among the valid data. We present two processing techniques that apply to both count-based and time-based windows. The first one adapts conceptual partitioning, the best existing method for continuous NN monitoring over update streams, to the sliding window model. The second technique reduces the problem to skyline maintenance in the distance-time space and precomputes the future changes in the NN set. We analyze the performance of both algorithms and extend them to variations of NN search. Finally, we compare their efficiency through a comprehensive experimental evaluation. The skyline-based algorithm achieves lower CPU cost, at the expense of slightly larger space overhead. Index Terms—Location-dependent and sensitive, spatial databases, query processing, nearest neighbors, data streams, sliding windows.
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