D. Chatziantoniou and K. A. Ross. Querying multiple features of groups in relational databases. In Proceedings of the International Conference on Very Large Databases, pages 295--306, 1996.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....that handles relation valued variables. To the best of our knowledge, the first reference to this operator and its implementation in Microsoft SQL Server 2000 appeared in [12] The notion of binding variables to sets of It is called SegmentApply in [12] tuples has also been proposed in [5, 6]. Interestingly, the motivation in this previous work was to support data warehousing applications. In this respect our work adds weight to the claim that such an operator is an important addition to relational query evaluation engines. 2. Even with the GApply operator added to the query ....

....part partsupp join union all scan group aggregate group scan partition NL table valued param table valued param Logical operation Physical operation Figure 2: Execution of GApply For instance, query Q1 is represented in our algebra as shown to the left in Figure 2. As opposed to [5], we allow only traditional relational operations in the per group query. Adding new operators that perform multiple aggregations more e#ciently is an orthogonal extension but is not the focus of this paper. Finally, pursuing the terminology of [6] we refer to the operation of GApply as groupwise ....

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D. Chatziantoniou and K. A. Ross. Querying multiple features of groups in relational databases. In VLDB, 1996.

....Sales sum in 100 Figure 1: The Data Cube data cube generalizes the traditional SQL syntax, there are yet many types of aggregate queries that are still hard to be expressed in SQL, like for instance queries involving grouping and aggregation over the same groups. Chatziantoniou and Ross in [CR96] propose another extension to SQL syntax that allows the succinct representation of aggregate queries involving, potentially repeated, selection, grouping and aggregation over the same groups. In technical terms, the Cube is a redundant multidimensional projection of a relation. It computes all ....

D. Chatziantoniou and K. A. Ross. Querying Multiple Features of Groups in Relational Databases. In Proceedings of the 22th VLDB Conference, pages 295--306, Bombay, India, 1996.

.... 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 data. An example correlated aggregate from a network management ....

D. Chatziantoniou and K. A. Ross. Querying multiple features of groups in relational databases. In Proceedings of VLDB, 1996.

....approach called AXL is described in [24] and its usage in data mining is discussed. Several extensions to the classic group by operator of SQL were proposed. Probably the most important extension is the data cube operator presented in [10] which is now support in some commercial systems. In [2] an additional such that clause for the group by operator is proposed introducing variables that range over a group and can be qualified by the such that clause. Red Brick s RISQL (now Informix) allows functions in the group by clause and supports several predefined aggregation functions, e.g. ....

D. Chatziantoniou and K.A. Ross. Querying multiple features of groups in relational databases. In T.M. Vijayaraman, A.P. Buchmann, C. Mohan, and N.L. Sarda, editors, Proc. of 22th Int. Conf. on Very Large Data Bases (VLDB'96), Mumbai (Bombay), India, pages 295--306. Morgan Kaufmann, 1996.

....approach called AXL is described in [22] and its usage in data mining is discussed. Several extensions to the classic group by operator of SQL were proposed. Probably the most important extension is the data cube operator presented in [10] which is now support in some commercial systems. In [2] an additional such that clause for the group by operator is proposed introducing variables that range over a group and can be qualified by the such that clause. Red Brick s RISQL (now Informix) allows functions in the group by clause and supports several predefined aggregation functions, e.g. ....

D. Chatziantoniou and K.A. Ross. Querying multiple features of groups in relational databases. In T.M. Vijayaraman, A.P. Buchmann, C. Mohan, and N.L. Sarda, editors, Proc. of 22th Int. Conf. on Very Large Data Bases (VLDB'96), Mumbai (Bombay), India, pages 295--306. Morgan Kaufmann, 1996.

....this approach called AXL is described in [23] and its usage in data mining is discussed. Several extensions to the classic group by operator of SQL were proposed. Probably the most important extension is the data cube operator presented in [9] which is now support in some commercial systems. In [2] an additional such that clause for the group by operator is proposed introducing variables that range over a group and can be qualified by the such that clause. Red Brick s RISQL (now Informix) allows functions in the group by clause and supports several predefined aggregation functions, e.g. ....

D. Chatziantoniou and K.A. Ross. Querying multiple features of groups in relational databases. In T.M. Vijayaraman, A.P. Buchmann, C. Mohan, and N.L. Sarda, editors, Proc. of 22th Int. Conf. on Very Large Data Bases (VLDB'96), Mumbai (Bombay), India, pages 295--306. Morgan Kaufmann, 1996.

....by default. However, we also allow the use of predicates like SORT BY column or SORT BY Example 12. The SPRINT Algorithm in AXL [ 1] AGGREGATE sprint(iNode INT, RecId INT, iCol INT, iValue REAL, iYorN INT) 2] f [ 3] TABLE treenodes(RecId INT, Col INT, Value REAL, YorN INT, KEY(Col, Value) [ 4] TABLE summary(Col INT, SplitGini REAL, SplitVal REAL, Yc INT, Nc INT) 5] TABLE split(RecId INT, LeftOrRight INT, KEY (RecId) 6] TABLE mincol(Col INT, Value REAL, Gini REAL) 7] TABLE node(Node INT) AS VALUES(iNode) 8] 9] INITIALIZE : ITERATE : f [10] INSERT INTO treenodes ....

....be added to AXL, providing opportunities for distributed and parallel data mining. Example 13. Categorical Classifier Expressed in AXL [ 1] AGGREGATE classify(RecId INT, iNode INT, iCol INT, iValue INT, iYorN INT) 2] f [ 3] TABLE treenodes(RecId INT, Node INT, Col INT, Value INT, YorN INT) [ 4] TABLE mincol(Col INT, MinGini REAL) 5] TABLE summary(Col INT, Value INT, Yc INT, Nc INT, KEY fCol,Valueg) 6] TABLE ginitable(Col INT, Gini REAL) 7] 8] INITIALIZE : ITERATE : f [ 9] INSERT INTO treenodes [10] VALUES(RecId, iNode, iCol, iValue, iYorN) 11] UPDATE summary [12] ....

D. Chatziantoniou and K. A. Ross, "Querying Multiple Features of Groups in Relational Databases."Proceedings of the 1996 VLDB Conference, September 1996.

.... dissemble(Outlook,Temp,Humidity,Wind,Play) AS (Col, Val, YorN) FROM PlayTennis) AS t; Example 8 Using Recursive Aggregates to Implement a Classifier in AXL [ 1]AGGREGATE classify(RecId INT, iNode INT, iCol INT, 2] iValue INT, iYorN INT) 3] 4] TABLE treenodes(RecId INT, Node INT, [ 5] Col INT, Value INT, YorN INT) 6] TABLE mincol(Col INT) 7] TABLE summary(Col INT, Value INT, Yc INT, Nc INT, 8] KEY fCol,Valueg) 9] TABLE ginitable(Col INT, Gini INT) 10] 11] INITIALIZE : ITERATE : f [12] INSERT INTO treenodes [13] VALUES(RecId, iNode, iCol, iValue, iYorN) ....

.... 0 [38] AS m [39] WHERE t.RecId = m.RecId [40] GROUP BY m. Value; 41] 42] 5 Group By Modifiers Powerful aggregate extensions based on modifications and generalizations of group by constructs have recently been proposed by researchers, OLAP vendors, and standard committees [5, 25]. Here, we show how these aggregate extensions can also be expressed in AXL, as an alternative and more flexible mechanism to achieve their advanced functionality. Consider the following query to an employee relation: 0 10 20 30 40 50 60 0 1000 2000 3000 4000 5000 6000 Number of Records ....

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D. Chatziantoniou and K. A. Ross, "Querying Multiple Features of Groups in Relational Databases." Proceedings of the 1996 VLDB Conference, September 1996.

....by default. However, we also allow the use of predicates like SORT BY column or SORT BY Example 12. The SPRINT Algorithm in AXL [ 1] AGGREGATE sprint(iNode INT, RecId INT, iCol INT, iValue REAL, iYorN INT) 2] f [ 3] TABLE treenodes(RecId INT, Col INT, Value REAL, YorN INT, KEY(Col, Value) [ 4] TABLE summary(Col INT, SplitGini REAL, SplitVal REAL, Yc INT, Nc INT) 5] TABLE split(RecId INT, LeftOrRight INT, KEY (RecId) 6] TABLE mincol(Col INT, Value REAL, Gini REAL) 7] TABLE node(Node INT) AS VALUES(iNode) 8] 9] INITIALIZE : ITERATE : f [10] INSERT INTO treenodes ....

....be added to AXL, providing opportunities for distributed and parallel data mining. Example 13. Categorical Classi er Expressed in AXL [ 1] AGGREGATE classify(RecId INT, iNode INT, iCol INT, iValue INT, iYorN INT) 2] f [ 3] TABLE treenodes(RecId INT, Node INT, Col INT, Value INT, YorN INT) [ 4] TABLE mincol(Col INT, MinGini REAL) 5] TABLE summary(Col INT, Value INT, Yc INT, Nc INT, KEY fCol,Valueg) 6] TABLE ginitable(Col INT, Gini REAL) 7] 8] INITIALIZE : ITERATE : f [ 9] INSERT INTO treenodes [10] VALUES(RecId, iNode, iCol, iValue, iYorN) 11] UPDATE summary [12] ....

D. Chatziantoniou and K. A. Ross, \Querying Multiple Features of Groups in Relational Databases."Proceedings of the 1996 VLDB Conference, September 1996.

....functions taking a set of tuples as argument and producing a single value as result. Our approach is more general than Klug s one, since the MultiDimensional model subsumes the relational one. Furthermore we consider, in addition to aggregate functions, also scalar functions. Many authors [5,11,19,23] claim that SQL is unsuited to data analysis applications, since some aggregate and grouping queries are difficult to express and optimize. They thus consider the problem of extending SQL with aggregation and analysis oriented operators that are more powerful, but also specific to particular ....

....to express and optimize. They thus consider the problem of extending SQL with aggregation and analysis oriented operators that are more powerful, but also specific to particular application domains. Gray et al. 11] propose cube as an operator generalizing group by. Chatziantoniou and Ross [5] extend both SQL and the relational algebra with an operator, dealing with aggregation variables , to succinctly express common queries, providing also a basis for improved query optimization. Rao et al. 19] consider the issue of supporting quantified queries, a class of queries that is ....

D. Chatziantoniou and K. Ross. Querying multiple features of groups in relational databases. In Twenty-second Int. Conf. on Very Large Data Bases, Bombay, pages 295--306, 1996.

....from the Endowment. Proceedings of the 25th VLDB Conference, Edinburgh, Scotland, 1999. 1 Introduction Two key aspects of OLAP queries are aggregation and dimension hierarchies. Aggregations can involve multiple GROUP BYs as in CUBE, ROLLUP, and DRILLDOWN [8] or multiple levels of granularity [5, 20]. Several algorithms have been proposed for the efficient implementation of these queries (see, e.g. 8, 5, 9, 1, 23, 19, 20] In contrast, work on dimension hierarchies has been sparse (see Section 1.2 for details) Dimension hierarchies arise naturally and are central to a large class of ....

....key aspects of OLAP queries are aggregation and dimension hierarchies. Aggregations can involve multiple GROUP BYs as in CUBE, ROLLUP, and DRILLDOWN [8] or multiple levels of granularity [5, 20] Several algorithms have been proposed for the efficient implementation of these queries (see, e.g. [8, 5, 9, 1, 23, 19, 20]) In contrast, work on dimension hierarchies has been sparse (see Section 1.2 for details) Dimension hierarchies arise naturally and are central to a large class of useful OLAP queries. In fact, ROLLUP and DRILLDOWN queries make sense only if there are dimension hierarchies with more than one ....

D. Chatziantoniou and K. A. Ross. Querying multiple features of groups in relational databases. In Proceedings of the International Conference on Very Large Databases, pages 295--306, 1996.

.... Now, UDAs are preferable to scratchpad functions for the following reasons: ffl UDAs (because of the presence of group by, and other reasons) are more amenable to parallelization and query optimization than user defined scalar functions; ffl Through the use of Supergroups and such that [8] each UDA in fact generates a family of column functions thus reducing the number of UDAs needed; ffl Through the composition and cascading of UDAs, complex datamining algorithms can be expressed in a declarative fashion, while preserving performance. The main benefit of this UDA centered ....

D. Chatziantoniou and K. A. Ross. "Querying Multiple Features of Groups in Relational Databases". VLDB 1996.

.... a c 3 6 b c 3 6 c c 3 8 b c 2 1 a f 2 1 b f 2 3 c f 2 5 d f 2 9 e f 2 9 f f If we let T be this result, notice that the SQL query: SELECT g,MAX(x) FROM R GROUP BY g is equal to Distinct( g;MAX(x) T ) is similar to, yet distinct from, the Phi operator defined by Chatziantoniou and Ross in [1]. The Phi operator was also introduced to define aggregation windows, although for different motivating problems. We defined because it allows a more natural treatment of SRQL. As described in Section 4.3, SRQL currently restricts the use of to ensure efficient evaluation. We are ....

D. Chatziantoniou and K. A. Ross. Querying multiple features of groups in relational databases. In Proceedings of the 22nd VLDB Conference, Mumbai, India, 1996.

....is on efficient query processing. This area is starting to receive the attention it deserves. A number of conventional relational query processing approaches have been applied to or extended for answering OLAP queries. Some of this work has concentrated on efficiently performing GROUP BY [8, 9, 20], aggregation [10, 23, 33, 30, 50, 68, 69] join or range queries [32, 60, 64] or supporting incomplete query answers [6, 29, 66] Several approaches have been proposed for supporting the SQL CUBE operator, including [2, 17, 23, 42, 53, 58] Yet another facet of query processing that has received ....

D. Chatziantoniou and K.A. Ross. Querying multiple features of groups in relational databases. In Proc. 22nd VLDB Conf., Mumbai, India, 1996.

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D. Chatziantoniou and K. A. Ross. Querying multiple features of groups in relational databases. In Proceedings of the International Conference on Very Large Databases, pages 295--306, 1996.

....Project 1 Faculty: Ross. The focus of the Columbia Fast Query Project is to process complex queries e#ciently. Ideally, we aim for interactive query response. However, we also aim to improve the performance of noninteractive queries over huge datasets. 2. 1 Complex OLAP Query Processing In [1] we present the notion of multi feature queries. Multi feature queries succinctly express complex queries such as Find the total sales among minimum price suppliers of each item. Such queries need multiple views and or subqueries in standard SQL. We demonstrate significant performance ....

D. Chatziantoniou and K. A. Ross. Querying multiple features of groups in relational databases. In Proceedings of the International Conference on Very Large Databases, pages 295--306, 1996.

....and its semantics. We give the details of the evaluation algorithm in Section 3 and present several optimizations in Section 4. Our implementation and performance results are discussed in Section 5. We conclude in Section 6 presenting related and future work. 2. Proposed Syntax and Semantics In [6] we have introduced the concept of multi feature queries which has proven useful for certain OLAP and datacube queries[18] In this section we extend slightly this syntax, covering however a significantly larger class of data analysis queries. These queries are called extended multifeature ....

....clause. 2 Although the relational algebra semantics are complicated, there is a direct mapping to a simple evaluation algorithm as it is shown in Section 3. Note that the result may have many duplicate rows due to the join in the last step of Definition 2.2. This topic is discussed in length in [6]. One solution to this problem is to get the join only of the grouping variables (X x i s) and or the aggregates (F x i s) mentioned in the select clause. Another issue concerns empty grouping variables. According to the previous definition, if a grouping variable of a group is empty, there ....

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D. Chatziantoniou and K. Ross. Querying Multiple Features of Groups in Relational Databases. In 22nd VLDB Conference, pages 295--306, 1996.

....it is also possible to compute aggregates at several coarser levels of granularity at the same time as computing aggregates at finer levels of granularity. Such algorithms are presented in [GBLP96, AAD 96, ZDN97, RS97] A different kind of decision support query has been considered in [CR96] involving aggregation queries in which multiple dependent aggregates are computed within each group. An example of such a query is the following: Q0: For each item, find its minimum price in 1996, and the total sales among all minimum price tuples. CR96] presented an extended SQL syntax that ....

....support query has been considered in [CR96] involving aggregation queries in which multiple dependent aggregates are computed within each group. An example of such a query is the following: Q0: For each item, find its minimum price in 1996, and the total sales among all minimum price tuples. CR96] presented an extended SQL syntax that allows a succinct representation of such queries. An experimental study demonstrated that such queries can be efficiently evaluated. In contrast, standard SQL representations of the same queries are verbose and redundant, leading to queries that are hard to ....

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D. Chatziantoniou and K. A. Ross. Querying multiple features of groups in relational databases. In Proceedings of VLDB, pages 295--306, 1996.

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D. Chatziantoniou and K. Ross. Querying multiple features of groups in relational databases. In Proc. 22nd Very Large Data Base Conf., 1996.

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D. Chatziantoniou and K. Ross. Querying multiple features of groups in relational databases. In Twenty-second Int. Conf. on Very Large Data Bases, Bombay, pages 295#306, 1996.

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D. Chatziantoniou and K. A. Ross. "Querying Multiple Features of Groups in Relational Databases". VLDB 1996.

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