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

By S. Muthukrishnan

Facts movement algorithms as an energetic learn time table emerged in basic terms over the last few years, even supposing the concept that of creating few passes over the information for acting computations has been round because the early days of Automata conception. the knowledge movement time table now pervades many branches of laptop technology together with databases, networking, wisdom discovery and information mining, and platforms. is in synch too, with facts circulate administration platforms (DSMSs) and unique to accommodate info speeds. Even past machine technology, facts circulate matters are rising in physics, atmospheric technological know-how and records. info Streams: Algorithms and purposes makes a speciality of the algorithmic foundations of knowledge streaming. within the info move situation, enter arrives very quickly and there's constrained reminiscence to shop the enter. Algorithms need to paintings with one or few passes over the information, area under linear within the enter dimension or time considerably lower than the enter dimension. some time past 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 on metric embeddings, pseudo-random computations, sparse approximation thought and conversation complexity. The functions for this situation comprise IP community site visitors research, mining textual content message streams and processing sizeable facts units typically. info Streams: Algorithms and functions surveys the rising region of algorithms for processing facts streams and linked functions. an intensive bibliography with over two hundred entries issues the reader to additional assets for exploration.

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For each pi , form groups 0 mod pi , . . , pi − 1 mod pi , called pi -groups. Each of the items in the domain now belong to one pi group for each i. The claim is, for any k toppers, each one of them will be isolated in 168 Foundations: Basic Algorithmic Techniques at least one of these groups, away from the other k − 1 toppers. This is true because any such topper α can collide with a different topper β in at most logk N pi -groups with different i ’s. Otherwise, the difference |α − β| < N would be divisible by logk N + 1 different primes > k which is a contradiction.

Therefore, the parsing gives a hierarchical way to reduce the string sizes of two strings independently while controlling the loss of quality in parsing into similar substrings. The parsing can be done in O(N log∗ N ) time. This parsing has found many applications to compression [194], edit distance computation [193], dynamic string matching [195], communication-efficient string exchanges [63], string nearest neighbors [178], streaming embedding [53], etc. The interest to us here is that the parsing and embedding that underlies many of these applications can be done in the Time Series model by keeping the “straddling” of the parsing at each level of the tree, similar to the wavelet example.

No matter what alternative is used, the approximation is weak since inner-product estimation is a difficult problem in the communication complexity setting captured by the small space constraint of the data stream models. Problem 3. Provide improved estimates for Lp -sums including distinct element estimation if input stream has statistical properties such as being Zipfian. Results are known for estimating the L2 -sum [59] and top-k [36] when the input is Zipfian, heavy-hitters [168] and heavy-hitters under “random, small tail” [164], but in general, only a handful of results are known that improve upon the worst case bounds.

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