J. Gray, S. Chaudhuri, A. Bosworth, A. Layman, D. Reichart, M. Venkatro, F. Pellow, and H. Pirahesh. Data cube: A relational operator generalizing group-by, cross-tab, and sub-totals. In In Data Mining and Knowledge Discovery 1, pages 29-53. Kluwer Academic Publishers, 1997.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....subsets of unsafe even MDR queries. Keywords: Inference Control, Privacy, OLAP 1 Introduction Multi dimensional range (MDR) query is an important class of decision support query in OLAP (On line Analytical Processing) systems [25] One of the most popular data models of OLAP systems, data cube [23], can be viewed as a collection of MDR queries. MDR queries are intended to assist users in exploring trends and patterns in large amount of data stored in data warehouses. Contrary to this initial objective, MDR queries can be used to obtain protected sensitive data, which results in the breach ....

....case any two out of the three queries are safe. Theorem 1 The MDQ problem is NP hard. # Restricted MDQ Problem Knowing that the MDQ problem is NP hard, is it possible to reduce the complexity with further restrictions We consider data cubes, a special class of MDR queries originally defined in [23]. In Definition 4 we rephrase the concepts of data cubes using MDR queries. Our definitions are equivalent to the original ones given in [23] We demonstrate those definitions in Example 4.5. The following Corollary 1 shows that the MDQ problem remains NP hard even when it is restricted to those ....

[Article contains additional citation context not shown here]

J. Gray, A. Bosworth, A. Layman, and H. Pirahesh. Data cube: A relational operator generalizing group-by, crosstab and sub-totals. In Proceedings of the 12th International Conference on Data Engineering, pages 152--159, 1996.

....penalty renders them impractical for OLAP systems. Unlike in statistical databases where queries are usually arbitrary, in OLAP systems queries usually comprise of well structured operations such as group by, cross tab and sub totals. Those operations are generalized by the data cube operator [21]. Traditional inference control mechanisms are computationally infeasible for OLAP systems partially because they ignore the unique structures of OLAP queries. As we shall show in this paper, efficient inference control is possible for data cube queries in OLAP systems. Table 1 shows a data cube ....

....they ignore the unique structures of OLAP queries. As we shall show in this paper, efficient inference control is possible for data cube queries in OLAP systems. Table 1 shows a data cube about employee salaries. The data cube is represented by a collection of twodimensional cross tabulations [21]. Each cross tabulation corresponds to a quarter of the year. The two dimensions are month and employee. Each internal cell of a cross tabulation contains the monthly salary value for an employee. We assume that individual salary values are sensitive and should be hidden from users, and therefore ....

[Article contains additional citation context not shown here]

J. Gray, A. Bosworth, A. Layman, and H. Pirahesh. Data cube: A relational operator generalizing group-by, crosstab and sub-totals. In Proceedings of the 12th International Conference on Data Engineering, pages 152--159, 1996.

....are common in statistical databases, OLAP queries usually comprise of well structured operations such as group by, cross tab and sub totals. Those operations can conveniently be integrated with data cube operator and various data cube operations, such as slicing dicing, roll up and drill down [20]. We will show how the limited formats and predictable structures of the OLAP queries as well as the multi dimensional hierarchical data model of OLAP systems can be exploited to simplify inference control. Table 1 shows a small two dimensional data set about monthly employee salaries. Individual ....

.... 2) Both have four different values that are mapped to the integer interval [1, 4] The full core cuboid C f is [1, 4] 1, 4] The core cuboid C c contains totally nine tuples and seven tuples are missing from C c (shown as N a in C c ) To define aggregates of a data cube, we follow [20] to augment each dimension with a special value ALL, for which we use symbol . Each aggregation vector is similar to a tuple except that it is formed with the augmented dimensions. An aggregation vector selects a set of tuples in core cuboids with its values, which form its aggregation set. All ....

J. Gray, A. Bosworth, A. Layman, and H. Pirahesh. Data cube: A relational operator generalizing group-by, crosstab and sub-totals. In Proceedings of the 12th International Conference on Data Engineering, pages 152--159, 1996.

....data, especially of data cubes. This decision differs from other existing approaches to integrate spatial and statistical data. Persistent analysis units and predicate based adhoc aggregation: Given the expected cardinalities of qualifying attributes and domains, a complete analysis data cube [8] would not be practical. On the contrary, the management of aggregated data has to be demand driven and therefore connected to the analysis units of the system. Further, because of the interactive exploration process, it is not restricted to predefined hierarchies of the aggregates but ad hoc and ....

J. Gray, A. Bosworth, A. Layman, and H. Pirahesh. Data Cube: A relational operator generalizing group-by, crosstab, and sub-totals. In Proceedings of the 12th International Conference on Data Engineering, 1996.

....60 220 220 100 100 60 10 10 110 170 150 sales time nuts bolts east south north west screws Figure 16. Roll up The operation describing the consolidation of a cube (i.e. the computation of every aggregation according to every level of every dimension) is called data cube [GRA 96] and can be seen as the generalization of the roll up operation. Figure 17 illustrates the result of such an operation applied to the cube sales (e.g. the sum of 1996 sales for all parts and all regions is 420) 3.2.1.2. Drill down The second operation, called drill down , consists in ....

GRAY J., BOSWORTH A., LAYMAN A., PIRAHESH H., "Data Cube : a relational operator generalizing group-by, cross-tab, and sub-totals", Proc. 12th ICDE, New Orleans, LO, Feb. 1996, p. 152--159.

....State Province State Province Store City PoliticalDiv. Country All (D) CityUSA CityCanada StoreUSA StoreCanada (B) A) C) Fig. 1. A) B) C) Three alternative dimension hierarchies for the location dimension. D) An instance of the location dimension. 1. 2 Summarizability Data cubes [GBLHP96] comprise the computation of a set of aggregate views, called cube views, which represent facts aggregated at different granularities (set of levels taken from a set of dimensions) Different fundamental functionalities for OLAP, like aggregate navigation, cube computation, and cube maintenance ....

....derive any cube view defined at a level l 2 from a cube view defined at a level l 1 by aggregating using the rollup functions between l 1 and l 2 of a particular dimension. In order to allow summarizability the data cube must be distributive, i.e. its aggregate functions must be distributive [GBLHP96] A distributive aggregate function af can be computed on a set by partitioning the set into disjoint subsets, aggregating each separately, and then computing the aggregation of these partial results with another aggregate function 1 that we denote by af c . The central problem we address in ....

J. Gray, A. Bosworth, A. Layman, and H. H. Pirahesh. Data cube : A relational operator generalizing group-by, cross-tab and sub-totals. In Proceedings of the 12th IEEE-ICDE Conference, New Orleans, Los Angeles, USA, 1996.

....Web sites, for example the well known Yahoo site, support only this type of loose integration. The area of On Line Analytical Processing (OLAP) which includes data analysis and decision support systems along with multidimensional databases, also deals with many of the problems we are addressing [GBLP95, CC94] These systems group together subsets of the database and present aggregates and common features of the data items in each group. A user may drill down into a set of data by successively restricting one or more of the attributes, while the system presents aggregates and summaries of the ....

.... we have built upon techniques from declarative query languages (including visual query languages [Cru94, VAO93] along with paradigms for navigating, summarizing and understanding data which are drawn largely from the arena of data analysis applications including multidimensional databases [CC94, GBLP95] and hypertext query interfaces [CT89] Our approach permits both the use of conventional declarative queries and the use of navigational techniques, including drill down and roll up operators (explained below) The novelty of our approach stems from the seamless integration of these different ....

J. Gray, A. Bosworth, A. Layman, and H. Pirahesh. Data Cube: A Relational Operator Generalizing Group-By, Cross-Tabs and Sub-Totals. To appear in IEEE Transactions on Knowledge and Data Engineering, 1995.

....but rather functions of the history of the underlying data. Relevant areas of research here certain ly include tempora l databases [18 ] as well as work on efficient monitoring of historical information [5] ffl Data warehouses also tend to contain highly aggregated and summarized information [7]. Although in some cases aggregations may be describable in a conventional view definition language, the expressiveness of aggregates and summary operators in such languages are lim ited, so more expressive view definition languages may be needed. Furthermore, efficient view maintenance in the ....

....view definition language, the expressiveness of aggregates and summary operators in such languages are lim ited, so more expressive view definition languages may be needed. Furthermore, efficient view maintenance in the presence of aggregation and summary information appears to be an open problem [7, 17]. ffl The information sources updating the base data generally operate independently from the warehouse where the view is stored, and the base data may come from legacy systems that are unab le or unwilling to participate in view maintenance. Most materialized view maintenance techniques rely on ....

J. Gray, A. Bosworth, A. Layman, and H. Pirahesh. Data Cube: A relational operator generalizing group-by, cross-tabs and sub-totals. IEEE Transactions on Knowledge and Data Engineering, 1995. To appear.

....data sources are modelled and implemented as data cubes classified and aggregated along different dimensions. Efficient data access and manipulation (roll up, drill down, slice and dice) as demanded in currently discussed OLAP applications and Data Warehouse environments ( 4] 3] 19] 6] [5]) combined with application specific data analysis procedures are provided. Different types of metadata associated with the data sets will guide search and data processing. For selecting and combining data, cf. Fig. 2) on top of the MDD mapping layer there will be a visual query language ....

J. Gray, A. Bosworth, A. Layman, and H. Pirahesh. Data Cube: A relational operator generalizing group-by, cross-tab, and sub-totals. In Proceedings of the 12th International Conference on Data Engineering, pages 152--159, 1996.

....has to consider this aspect to provide reuse of already computed results, especially aggregated values to improve performance. A demand driven and to analysis units connected approach for the management of aggregated data would be much better suited than a solution based on a complete data cube [5]. Unlike in the usual scenarios the cardinalities of the category attributes and their domains lead to the conclusion that a complete data cube would be not practicable in our application, as it will not be in a lot of other scientific applications. The approach should consider representative ....

....due to the process of incoming records on cancer cases it could happen that there is a considerable time interval between the date of diagnosis and registration date. The case of occuring updates has to be considered. So already established techniques (as mentioned before the complete data cube [5]) for reuse and storage of aggregates do not meet the requirements. ffl dynamic ad hoc aggregation support for an integrated view, multidimensional data processing and especially global query optimization. On such a basis empirical studies have to be carried out to compare and evaluate the ....

J. Gray, A. Bosworth, A. Layman, and H. Pirahesh. Data Cube: A relational operator generalizing group-by, crosstab, and sub-totals. In Proceedings of the 12th International Conference on Data Engineering, pages 152--159, 1996.

..... 7 2.1 A Star Schema [CD97] 14 2.2 A Snowflake Schema [CD97] 15 2.3 Data Warehousing Architecture [CD97] 16 2. 4 The CUBE operator for 0D, 1D, 2D, and 3D datacubes [GBLP96] 20 2.5 The eight TPC D views where P for part, S for supplier, and C for customer [HRU96] 23 2.6 A four attribute Minimum Spanning Tree [AAD 96] 29 2.7 (a) MMST for dimension order ABCD (b) MMST for dimension ....

....records in isolation. DSS queries thus make heavy use of aggregations, and the ability to simultaneously aggregate across many sets of dimensions (in SQL terms, this translates to many simultaneous groupbys) is very crucial for OLAP or multidimensional data analysis applications. Gray, et al. [GBLP96] introduced the CUBE operator as the extension to the SQL s SELECT GROUP BY HAVING syntax. It is equivalent to the union of a number of standard groupby operations, which computes groupby aggregations over all possible subsets of the specified dimensions. Its rapid acceptance has made the SQL ....

[Article contains additional citation context not shown here]

J. Gray, A. Bosworth, A. Layman, and H. Pirahesh. Data cube: A relational operator generalizing group-by, cross-tab and sub-totals. In Proc. 1996 Int'l Conf. Data Engineering, pages 152--159, New Orleans, Louisiana, Feb. 1996.

....An user may ask for total sales by product, by region, or by product and region. In order to speed up queries we could precompute some aggregates in advance and materialize them, or we can materialize the whole cube. This last approach is the motivation for the Data Cube Operator, introduced in [GBPL97]. A Relational Database is not the best data structure to hold data which is, in nature, multidimensional. Let us look at an instance of the RegionSales relation : Product Region Sales p1 r1 100 p1 r2 105 p1 r3 100 . p3 r1 30 p3 r2 40 p3 r3 50 We see that there is one attribute ....

J. Gray, A. Bosworth, A. Layman, and H. Pirahesh. Data Cube : A Relational Operator Generalizing Group-By, Cross-Tab and Sub-Totals. Data Mining and Knowledge Discovery 1, 29-53, 1997.

....and GBottomD a level group containing the bottom levels of each dimension in D. We also define a base fact table as a fact table with schema (fname; GBottomD ; m) 2.2 Data Cubes Several classes of aggregate views have been used to fulfill different requirements in OLAP systems. Gray et al. [5] introduced the data cube operator as a shorthand for a set of cube views that contains data from a base fact table, aggregated over all the possible groups of attributes in it. We will extend it in order to to include views computing aggregates over the levels of the dimensions , and define the ....

J. Gray, A. Bosworth, A. Layman, and H. H. Pirahesh. Data cube : A relational operator generalizing group-by, cross-tab and sub-totals. Data Mining and Knowledge Discovery 1, pgs. 29-53, 1997.

....of queries. This approach of materializing needed aggregates is possible only when the expected set of queries is known in advance. Specifically, the OLAP approach addresses queries that group by different combinations of columns, known as dimensions. Such queries are called Datacube queries in [GBLP96]. But when ad hoc queries must be issued that filter the rows by selection criteria that are not part of the dimensional scheme, summary tables that do not foresee such filtering cannot be used. In these cases the queries must be evaluated by accessing other indexes on the base data. Example 1.1. ....

....for which we might create a Projection index, Value List index, or Bit Sliced index, and AGG is an aggregate function, such as COUNT, MAX, MIN, etc. 3. 2] SELECT AGG(C) FROM T WHERE condition; 12In what follows, we usually consider only aggregate functions that are Distributive or Algebraic [GBLP96]. A Distributive function is a function that can be applied to subsets of the input and the results combined to compute the answer for the entire set. The aggregate functions COUNT, SUM, MIN, and MAX are distributive aggregate functions. Algebraic functions are evaluable using other distributive ....

[Article contains additional citation context not shown here]

Jim Gray, Adam Bosworth, Andrew Layman, and Hamid Pirahesh. Data Cube: A Relational Operator Generalizing Group-By, Cross-Tab, and Sub-Totals. Proceedings of the 12th International Conference on Data Engineering, pp. 152-159, 1996.

....Let us go back to Figure 2.4. The cuboid shown on that figure corresponds to the following SQL query: SELECT product, store, customer, SUM(sales) FROM Our sales GROUP BY product, store, customer In addressing the problem of a multiple scan two new operators Cube and Rollup have been proposed [24]. The Cube operator is the n dimensional generalization CHAPTER 2. RELATED WORK 20 of the group by operator. It computes group bys corresponding to all possible combinations of a list of dimensions (attributes) However, in some cases, it is not necessary to compute the full cube. In such cases, ....

J. Gray, A. Bosworth, A. Layman, and H. Pirahesh. Data cube: A relational operator generalizing group-by, cross-tab and sub-totals. In Proc. 1996 Int'l Conf. on Data Engineering, pages 152--159, New Orleans, Louisiana, Feb. 1996.

....IQ product currently provides both variant index types [EDEL95, FREN95] and recommends multiple indexes per column in some cases. Late in the paper, we introduce a new indexing approach to support OLAP type queries, commonly used in Data Warehouses. Such queries are called Datacube queries in [GBLP96]. OLAP query performance depends on creating a set of summary tables to efficiently evaluate an expected set of queries. The summary tables pre materialize needed aggregates, an approach that is possible only when the expected set of queries is known in advance. Specifically, the OLAP approach ....

.... SALES, containing sales data, together with dimension tables known as TIME (when the sales are made) PRODUCT (product sold) and CUSTOMER (purchaser in the sale) Most OLAP products do not express their queries in SQL, but much of the work of typical OLAP queries could be represented in SQL [GBLP96] (although more than one query might be needed) 5.1] SELECT P.brand, T.week, C.city, SUM(S.dollar sales) FROM SALES S, PRODUCT P, CUSTOMER C, TIME T WHERE S.day = T.day and S.cid = C.cid and S.pid = P.pid and P.brand = brandvar and T.week = datevar and C.state in ( Maine , New Hampshire , ....

Jim Gray, Adam Bosworth, Andrew Layman, and Hamid Pirahesh. Data Cube: A Relational Operator Generalizing Group-By, Cross-Tab, and Sub-Totals. Proc. 12th Int. Conf. on Data Eng., pp. 152-159, 1996.

.... statistical tests) or visualisation (map, graphic, table) The system provides application specific data analysis procedures as well as efficient data access and manipulation methods (e.g. roll up, drill down, slice and dice) demanded in OLAP applications and data warehouse environments [2, 4, 3]. Different types of metadata associated with the data sets guide the search and data processing. Multidimensional data management in general is examined in the field of statistical, temporal and spatial database systems [8, 6, 9, 11, 5] 12] describes a system that relates geocoded cancer cases ....

....analysis data, especially of data cubes. This decision differs from other existing approaches to integrate spatial and statistical data. ffl Persistent analysis units and predicate based ad hoc aggregation: Given the expected cardinalities of category attributes and domains, a complete data cube [3] would not be practical. On the contrary, the management of aggregated data has to be demand driven and therefore connected to the analysis units of the system. Further, because of the interactive exploration process, it is not restricted to predefined hierarchies of the aggregates but ad hoc and ....

J. Gray, A. Bosworth, A. Layman, and H. Pirahesh. Data Cube: A relational operator generalizing group-by, crosstab, and sub-totals. In Proceedings of the 12th International Conference on Data Engineering, 1996.

....often precompute aggregates at various levels of detail and on various combinations of attributes. Speed is critical for this precomputation as well, since the cost and speed of precomputation influences how frequently the aggregates are brought up to date. 1. 1 What is a CUBE Recently, [GBLP96] introduced the CUBE operator for conveniently supporting multiple aggregates in OLAP databases. The CUBE operator is the n dimensional generalization of the group by operator. It computes group bys corresponding to all possible combinations of a list of attributes. Returning to our retail ....

....query is to rewrite it as a collection of eight group by queries and execute them separately. There are several ways in which this simple solution can be improved. In this paper, we present fast algorithms for computing the data cube. We assume that the aggregating functions are distributive [GBLP96], that is, they allow the input set to be partitioned into disjoint sets that can be aggregated separately and later combined. Examples of distributive functions include max, min, count, and sum. The proposed algorithms are also applicable to the algebraic aggregate functions [GBLP96] such as ....

[Article contains additional citation context not shown here]

Jim Gray, Adam Bosworth, Andrew Layman and Hamid Pirahesh. Data Cube: A Relational Operator Generalizing Group-By, CrossTab and Sub-Totals. Proc. of the 12th Int. Conf. on Data Engineering, pp 152--159, 1996.

....information, and then contrast one category with another. There are four steps to such data analysis: formulating a query that extracts relevant data from a large database, extracting the aggregated data from the database into a file or table, # An extended abstract of this paper appeared in Gray et al. 1996). P1: RPS ASH P2: RPS Data Mining and Knowledge Discovery KL411 02 Gray March 5, 1997 16:21 30 GRAY et al. visualizing the results in a graphical way, and analyzing the results and formulating a new query. Visualization tools display data trends, clusters, and differences. Some of the most ....

....draft SQL standard (ISO IEC DBL:MCI 006, 1996) 2. It seems likely that a relational pivot operator will appear in database systems in the near future. P1: RPS ASH P2: RPS Data Mining and Knowledge Discovery KL411 02 Gray March 5, 1997 16:21 52 GRAY et al. 3. An earlier version of this paper (Gray et al. 1996) and the Microsoft SQL Server 6.5 product implemented a slightly different syntax. They suffix the GROUP BY clause with a ROLLUP or CUBE modifier. The SQL Standards body chose an infix notation so that GROUP BY and ROLLUP and CUBE could be mixed in a single statement. The improved syntax is ....

Gray, J., Bosworth, A., Layman, A., and Pirahesh, H. 1996. Data cube: A relational operator generalizing group-by, cross-tab, and roll-up. Proc. International Conf. on Data Engineering. New Orleans: IEEE Press.

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J. Gray, S. Chaudhuri, A. Bosworth, A. Layman, D. Reichart, M. Venkatro, F. Pellow, and H. Pirahesh. Data cube: A relational operator generalizing group-by, cross-tab, and sub-totals. In In Data Mining and Knowledge Discovery 1, pages 29-53. Kluwer Academic Publishers, 1997.

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J. Gray, A. Bosworth, A. Layman, and H. H. Pirahesh. Data cube : A relational operator generalizing group-by, cross-tab and sub-totals. In Proceedings of the 12th IEEE International Conference on Data Engineering, New Orleans, Los Angeles, USA, 1996.

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Jim Gray, Adam Bosworth, Andrew Layman, and Hamid Pirahesh. Data Cube: A relational operator generalizing group-by, cross-tabl and sub-totals. In Proceedings of the 12th International Conference on Data Engineering (ICDE '96), pages 152--159, 1996.

No context found.

J. Gray, S. Chaudhuri et. al.: Data Cube: A Relational Operator Generalizing Group-By, Cross-Tab and Sub-Totals. Data Mining and Knowledge Discovery Vol. 1, 1997

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J. Gray, S. Chaudhuri et. al.: Data Cube: A Relational Operator Generalizing Group-By, Cross-Tab and Sub-Totals. Data Mining and Knowledge Discovery Vol. 1, 1997

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J. Gray, S. Chaudhuri et. al.: Data Cube: A Relational Operator Generalizing Group-By, CrossTab and Sub-Totals. Data Mining and Knowledge Discovery Vol. 1, 1997

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