Phillip B. Gibbons and Yossi Matias. Synopsis data structures for massive data sets. DIMACS: Series in Discrete Mathematics and Theoretical Computer Science: Special Issue on External Memory Algorithms and Visualization, A, 1999.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....numbers of exact precision. Thus, random generators are used in [53]to tackle the problem of how to reduce the number of required random bits. The problem of approximating L p distances in one pass algorithms has a variety of other applications too, e.g. in estimating the size of self join [7, 45] and in the estimation of statistics of network ow data [42] Computing sketches is a technique used with success to get summaries of the data. It has enabled compression of data and speeding up computation for various data mining tasks [54, 32, 23, 24, 33] See also in section 5 for a ....

P. Gibbons and Y. Matias. Synopsis data structures for massive data sets. In SODA, pages S909{S910, 1999.

....rise to a family of approximation algorithms) it may give more insight into the problem in question. With the current trend of increasing memory and storage sizes, the problem of examining large structures in sublinear time has been studied in other contexts. For example, Gibbons and Matias [15, 16] develop a variety of data structures that glean information from large databases so they can be examined in sublinear time. Organization. This paper is organized as follows: In section 2 we present de nitions and terminology that will be used in the rest of the paper. In Section 3 we preset a ....

P. B. Gibbons and Y. Matias. Synopsis data structures for massive data sets. DIMACS: Series in Discrete Mathematics and Theoretical Computer Science: Special Issue on External Memory Algorithms and Visualization, A, 1999.

.... of the information quality of Web information sources (e.g. number of reviews per book in an e commerce site) as a basis for planning global queries in a Web mediator [27] 28] This broad importance of statistics management has led to a plethora of approximation techniques, for which [15] have coined the general term data synopses : advanced forms of histograms [30, 16, 20] spline synopses [22, 23] sampling [6, 17, 14] and parametric curve fitting techniques [34, 9] all the way to highly sophisticated methods based on kernel estimators [2] or Wavelets and other transforms [26, ....

P. B. Gibbons and Y. Matias. Synopsis Data Structures for Massive Data Sets. In Symposium on Discrete Algorithms, 1999.

.... data have attracted wide atten tion of networks, e commerce, information retrieval and databases [2, 19] In contrast, there have not been many studies on semi structured data min ing [1, 4, 7, 9, 13, 15, 16, 20, 22] There are a body of researches on online data processing and mining [10, 14, 18]. Most related work is Hidher [11] who proposed a model of continuous pattern discovery from unbounded data stream, and presented adaptive online algorithm for mining association rules. Parthasarathy et al. 17] and Mannila et al. 14] studied mining of sequential patterns and episode patterns. ....

P. B. Gibbons and Y. Matias, Synopsis Data Structures for Massive Data Sets, In External Memory Algorithms, DIMACS Series in Discr. Math. and Theor. Cornpt. Sci., Vol. 50, AMS, 39 70, 2000.

....and performance of applications in a wide area network. Used as index structures, it provides fast alternative access paths to the base data. Used as materialized views [85] in databases or data warehouses [82] it improves the performance of complex queries over the base data. Used as synopses [84], it provides fast, approximate answer to queries or statistics necessary for cost based query optimization. Derived data varies in complexity: It can be a simple copy of the base data, in the cases of caching and replication, or it can be the result of complex structural or content transformation ....

P. B. Gibbons and Y. Matias. Synopsis data structures for massive data sets. DIMACS Series in Discrete Mathematics and Theoretical Computer Science: Special Issue on External Memory Algorithms and Visualization, A:39--70, 1999.

....to monitor network tra#c behavior. The large volume of stream data, and the online nature of the various applications that operate on such data, make it imperative for the applications to compute a variety of summary information in an online fashion using a bounded amount of space (see, e.g. [1, 2, 4, 5, 6, 7, 8], and the references therein) Correlated aggregates (see, e.g. 3, 6] which provide a natural mechanism for the flexible composition of basic aggregates, are desirable since they are more descriptive than the basic aggregates for understanding relationships between variables in the stream ....

P. B. Gibbons and Y. Matias. Synopsis data structures for massive data sets. In Proceedings of SODA, 1999. 7

....DQT implementation. Data Mining. Geographic Information Systems (GIS) deal with data that exhibits spatio temporal correlations, but the processing is centralized, and algorithms are driven by the need to reduce search cost, typically by optimizing disk access latency. Some of these approaches ([23, 24, 26]) propose the construction of wavelet synopses, for fast processing of range sum queries. Many of the techniques proposed for approximate querying and data mining have informed the coding techniques that we choose in our system. An interesting example of a distributed infrastructure for wide area ....

Phillip B. Gibbons and Yossi Matias. Synopsis data structures for massive data sets. DIMACS: Series in Discrete Mathematics and Theoretical Computer Science: Special Issue on External Memory Algorithms and Visualization, A, 1999.

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P. B. Gibbons and Y. Matias. Synopsis data structures for massive data sets. DIMACS: Series in Discrete Math. and Theoretical Computer Science: Special Issue on External Memory Algorithms and Visualization, 1999.

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P. B. Gibbons and Y. Matias. Synopsis data structures for massive data sets. In J. M. Abello and J. S. Vitter, editors, External Memory Algorithms, pages 39--70. AMS, 1999. DIMACS: Series in Discrete Mathematics and Theoretical Computer Science, Vol. 50. A two page summary appeared as a short paper in SODA'99.

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GIBBONS, P. B., AND MATIAS, Y. Synopsis data structures for massive data sets. DIMACS: Series in Discrete Mathematics and Theoretical Computer Science: Special Issue on External Memory Algorithms and Visualization (1999).

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P. B. Gibbons and Y. Matias. Synopsis data structures for massive data sets. In J. M. Abello and J. S. Vitter, editors, External Memory Algorithms, pages 39-70. AMS, 1999. DIMACS: Series in Discrete Mathematics and Theoretical Computer Science, Vol. 50. A two page summary appeared as a short paper in SODA'99.

....whenever the self join sizes are smaller than n B. The performance and accuracy bounds of the algorithms in this paper are valid for any data distributions. Related work. Tracking algorithms and other general data reduction techniques have a long history; see [BDF 97] for a recent survey. GM99] presented a formal framework for evaluating such sublinear space synopsis data structures, and a survey of some of the results in this area. There has been a flurry of recent work in approximate query answering (e.g. VL93, Olk93, BDF 97, HHW97, GM98, AGPR99, HH99, VW99, IP99, AGP00, ....

P. B. Gibbons and Y. Matias. Synopsis data structures for massive data sets. In J. M. Abello and J. S. Vitter, editors, External Memory Algorithms, pages 39--70. AMS, 1999. DIMACS: Series in Discrete Mathematics and Theoretical Computer Science, Vol. 50. A two page summary appeared as a short paper in SODA'99.

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Phillip B. Gibbons and Yossi Matias. Synopsis data structures for massive data sets. DIMACS: Series in Discrete Mathematics and Theoretical Computer Science: Special Issue on External Memory Algorithms and Visualization, A, 1999.

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Phillip B. Gibbons and Yossi Matias. Synopsis data structures for massive data sets. DIMACS: Series in Discrete Mathematics and Theoretical Computer Science: Special Issue on External Memory Algorithms and Visualization,A, 1999.

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P. B. Gibbons and Y. Matias. Synopsis data structures for massive data sets. In Proceedings of the 10th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 909--910. ACM Press, 1999.

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P. B. Gibbons, and Y. Matias, "Synopsis Data Structures for Massive Data Sets," Series in Discrete Mathematics and Theoretical Computer Science: Special Issue on External Memory Algorithms and Visualization, A, 1999.

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P. B. Gibbons and Y. Matias. Synopsis data structures for massive data sets. DIMACS: Series in Discrete Mathematics and Theoretical Computer Science: Special Issue on External Memory Algorithms and Visualization, A, 1999.

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Phillip B. Gibbons and Yossi Matias. Synopsis data structures for massive data sets. DIMACS: Series in Discrete Mathematics and Theoretical Computer Science: Special Issue on External Memory Algorithms and Visualization, A, 1999.

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P. Gibbons and Y. Matias. Synopsis data structures for massive data sets. In DIMACS: Series in Discrete Mathematics and Theoretical Computer Science: Special Issue on External Memory Algorithms and Visualization, 1999.

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Phillip B. Gibbons and Yossi Matias. Synopsis data structures for massive data sets. DIMACS: Series in Discrete Mathematics and Theoretical Computer Science: Special Issue on External Memory Algorithms and Visualization, A, 1999.

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Phillip Gibbons and Yossi Matias. Synopsis data structures for massive data sets. In Proc. 10th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 909--910, 1999.

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P. Gibbons and Y. Matias. Synopsis data structures for massive data sets. Proc. SODA, pages S909-- S910, 1999.

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Phillip B. Gibbons and Yossi Matias. Synopsis data structures for massive data sets. DIMACS: Series in Discrete Mathematics and Theoretical Computer Science: Special Issue on External Memory Algorithms and Visualization, A, 1999.

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P. B. Gibbons and Y. Matias, Synopsis Data Structures for Massive Data Sets, In External Memory Algorithms, DIMACS Series in Discr. Math. and Theor. Compt. Sci., Vol. 50, AMS, 39--70, 2000.

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P. B. Gibbons and Y. Matias. Synopsis Data Structures for Massive Data Sets. Technical report, Bell Labs, 1998.

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