By Minos Garofalakis, Johannes Gehrke, Rajeev Rastogi

This quantity makes a speciality of the idea and perform of *data circulate management*, and the unconventional demanding situations this rising area poses for data-management algorithms, structures, and functions. the gathering of chapters, contributed by means of gurus within the box, deals a complete advent to either the algorithmic/theoretical foundations of knowledge streams, in addition to the streaming structures and functions inbuilt varied domains.

A brief introductory bankruptcy presents a short precis of a few uncomplicated info streaming recommendations and types, and discusses the main components of a accepted circulate question processing structure. for this reason, half I makes a speciality of easy streaming algorithms for a few key analytics features (e.g., quantiles, norms, subscribe to aggregates, heavy hitters) over streaming information. half II then examines very important concepts for uncomplicated move mining initiatives (e.g., clustering, class, widespread itemsets). half III discusses a couple of complicated subject matters on circulate processing algorithms, and half IV makes a speciality of approach and language facets of information circulation processing with surveys of influential method prototypes and language designs. half V then provides a few consultant purposes of streaming ideas in numerous domain names (e.g., community administration, monetary analytics). ultimately, the quantity concludes with an summary of present facts streaming items and new program domain names (e.g. cloud computing, immense info analytics, and intricate occasion processing), and a dialogue of destiny instructions during this interesting field.

The ebook offers a entire review of middle strategies and technological foundations, in addition to a number of structures and functions, and is of specific curiosity to scholars, academics and researchers within the quarter of information circulate administration.

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**Extra info for Data Stream Management: Processing High-Speed Data Streams**

**Example text**

Consider first the case r ≥ |S|−e. We have rminQ (q ) ≥ (1 − )|S|, and therefore i = has the desired property. We now focus on the case r < |S| − e, and start by choosing the smallest index j such that rmaxQ (qj ) > r + e. If j = 1, then j is the desired index since r + e < rmaxQ (q1 ) ≤ |S|. Otherwise, j ≥ 2, and it follows that r − e ≤ rminQ (qj −1 ). If r − e > rminQ (qj −1 ) then rmaxQ (qj ) − rminQ (qj −1 ) > 2e; a contradiction since e = maxi (rmaxQ (qi+1 ) − rminQ (qi ))/2. By our choice of j , we have rmaxQ (qj −1 ) ≤ r + e.

Stokes, Estimating the number of classes in a finite population. J. Am. Stat. Assoc. 93, 1475–1487 (1998) 49. M. Wu, C. Jermaine, A Bayesian method for guessing the extreme values in a data set, in Proc. 33rd VLDB (2007), pp. 471–482 50. P. Billingsley, Probability and Measure, 2nd edn. (Wiley, New York, 1986) 51. M. Law, Simulation Modeling and Analysis, 4th edn. (McGraw-Hill, New York, 2007) 52. E. Knuth, The Art of Computer Programming, vol. 2: Seminumerical Algorithms (AddisonWesley, Reading, 1969) 53.

4 Biased Sampling When using a biased sampling scheme, we can, in principle, recover an unbiased estimate of a population sum by using a Horvitz–Thompson (HT) estimator; see, for example, [3], where these estimators are called π -estimators. The general form of an HT-estimator for a population sum of the form θ = i∈W h(ei ) based on a sample S ⊆ W is θˆHT = i∈S (h(ei )/πi ), where πi is the probability that element ei is included in S. Assume that πi > 0 for each ei , and let Φi = 1 if ei ∈ S and Φi = 0 otherwise, so that E[Φi ] = πi .