By Minos Garofalakis, Johannes Gehrke, Rajeev Rastogi

This quantity makes a speciality of the idea and perform of *data move management*, and the radical demanding situations this rising area poses for data-management algorithms, platforms, and functions. the gathering of chapters, contributed through professionals within the box, bargains a finished creation to either the algorithmic/theoretical foundations of information streams, in addition to the streaming platforms and purposes inbuilt diverse domains.

A brief introductory bankruptcy offers a short precis of a few simple info streaming options and types, and discusses the major parts of a usual move question processing structure. in this case, half I specializes in simple streaming algorithms for a few key analytics capabilities (e.g., quantiles, norms, subscribe to aggregates, heavy hitters) over streaming facts. half II then examines vital concepts for uncomplicated flow mining initiatives (e.g., clustering, class, widespread itemsets). half III discusses a few complicated issues on circulation processing algorithms, and half IV specializes in process and language elements of information flow processing with surveys of influential process prototypes and language designs. half V then offers a few consultant purposes of streaming strategies in numerous domain names (e.g., community administration, monetary analytics). eventually, the quantity concludes with an summary of present information streaming items and new software 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 presents a finished assessment of center strategies and technological foundations, in addition to quite a few structures and purposes, and is of specific curiosity to scholars, teachers and researchers within the quarter of knowledge flow administration.

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

**Example text**

Denote by Xi the number of the i most recent arrivals in the window that have been inserted into the linked list: Xi = nj=n−i+1 Φj . J. Haas that if Xi = m for some m ≥ 0, then either Xi+1 = m or Xi+1 = m + 1. Moreover, it follows from our previous analysis that Pr{X1 = 1} = 1 and Pr{Xi+1 = mi + 1 | Xi = mi , Xi−1 = mi−1 , . . , X1 = m1 } = Pr{Φn−i = 1} = 1/(i + 1) for all 1 ≤ i < n and m1 , m2 , . . , mi such that m1 = 1 and mj +1 − mj ∈ {0, 1} for 1 ≤ j < i. Thus M = Xn is distributed as the number of successes in a sequence of n independent Poisson trials with success probability for the ith trial equal to 1/i.

10 We Data-Stream Sampling: Basic Techniques and Results 39 where σj2 = (1/(m − 1)) ei ∈Λj (h(ei ) − (θj /m))2 and θj = biased estimator of Var[θˆ ] is ˆ θˆ ] = m Var[ n −1 k h(ei ). An un- L σˆ j2 , j =1 2 ˆ ei ∈Sj (h(ei ) − (θj /m)) where σˆ j2 = (1/(r − 1)) ei ∈Λj and θˆj = (m/r) ei ∈Sj h(ei ). each σj2 is very Observe that if the strata are highly homogeneous, then small, so that Var[θˆ ] is very small. Indeed, it can be shown [1, Sect. 6] that if L 2 2 ˆ m L j =1 ((θj /m) − (θ/n)) ≥ (1 − (m/n)) j =1 σj , then the variance of θ under stratified sampling is less than or equal to the variance under simple random sampling.

Narasayya, On random sampling over joins, in Proc. ACM SIGMOD (1999), pp. 263–274 20. S. B. Gibbons, Y. Matias, A. Silberschatz, Bifocal sampling for skew-resistant join size estimation, in Proc. ACM SIGMOD (1996), pp. 271–281 21. V. L. Lee, R. Ramakrishnan, ICICLES: self-tuning samples for approximate query answering, in Proc. 26th VLDB (2000), pp. 176–187 22. J. N. Swami, Sampling-based selectivity estimation using augmented frequent value statistics, in Proc. Eleventh ICDE (1995), pp. 522–531 23.