Download Data Streams: Algorithms and Applications (Foundations and by S. Muthukrishnan PDF

By S. Muthukrishnan

Information move algorithms as an lively examine time table emerged simply during the last few years, although the idea that of constructing few passes over the information for appearing computations has been round because the early days of Automata conception. the knowledge circulation time table now pervades many branches of desktop technology together with databases, networking, wisdom discovery and knowledge mining, and platforms. is in synch too, with information circulate administration structures (DSMSs) and distinctive to house info speeds. Even past laptop technological know-how, facts flow matters are rising in physics, atmospheric technological know-how and information. info Streams: Algorithms and functions specializes in the algorithmic foundations of information streaming. within the info circulation state of affairs, enter arrives very quickly and there's restricted reminiscence to shop the enter. Algorithms need to paintings with one or few passes over the information, house under linear within the enter dimension or time considerably under the enter dimension. long ago few years, a brand new concept has emerged for reasoning approximately algorithms that paintings inside those constraints on area, time and variety of passes. a few of the equipment depend upon metric embeddings, pseudo-random computations, sparse approximation idea and conversation complexity. The purposes for this situation comprise IP community site visitors research, mining textual content message streams and processing immense information units normally. facts Streams: Algorithms and purposes surveys the rising zone of algorithms for processing facts streams and linked functions. an intensive bibliography with over two hundred entries issues the reader to extra assets for exploration.

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1 Group Testing This goes back to an earlier Paul and Carole game. Paul has an integer I between 1 and n in mind. ”. Carole determines various x’s, and Paul answers the questions truthfully. How many questions does Carole need, in the worst case? There is an entire area called Combinatorial Group Testing that produces solutions for such problems [80]. In the data stream case, each question is a group of items and the algorithm plays the role of Carole. This setup applies to a number of problems in data streams.

However, in applications to IP networks in earlier versions [81], it is used to determine a single S for {1, . . , N } and used for any T specified at the query time by projecting S on the given T . By asking for a sample which will provide such subset-sum estimates for any T , one has to necessarily settle for extremely weak accuracy guarantees in the worst case since the set of possible T ’s is exponential in ||A||1 . It is also not clear one needs to aim for such a general query since one needs to identify suitable applications where we need arbitrary subset sums – points or ranges seemed to be adequate for many applications thus far.

This is the only such dynamic sampling scheme we know. Problem 2. Say we have data streams over two observed variables (xt , yt ). An example correlated aggregate at time t is {g(yi ) | xi = f (x1 · · · xt )}, that is, computing some aggregate function g – SUM, MAX, MIN – on those yt ’s when the corresponding xt ’s satisfy certain relationship f . For what f ’s and g’s (by sampling or otherwise) can such queries be approximated on data streams? See [150] for the motivation. 2 Random Projections This approach relies on dimensionality reduction, using projection along pseudo-random vectors.

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