J. Albert. Algebraic properties of bag data types. In VLDB, 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....The data items, the tuples, are unordered, and the relations contain no duplicates, and cannot be nested. Relaxing these assumptions leads to numerous distinct data types, such as the complex objects (nested sets) Jac82, AB87, KV84, KRS85, AG91] the bags (sets with duplicates) BK90, Mum90, Alb91, BS91, GM93, LW94] the lists (internal order) the ordered sets, and the pomsets (partially ordered multisets) Pra84] 2.1 Partially Ordered Multisets Pomsets The pomset type generalizes sets, bags, lists, trees, and other ordered types, and therefore provides a uniform representation for ....

J. Albert. Algebraic properties of bag data types. In Proc. 17th Int'l Conf. on Very Large Data Bases, pages 211--219, 1991.

....schema constructs. The syntax of SIQL queries, q, is listed below (lines 1 to 12) D, D 1 : D n denote a bag of the appropriate type (base collections) The construct in line 1 is an enumerated bag of constants. is the bag union operator and Gamma Gamma is the bag monus operator [18]. group groups a bag of pairs on their first component. distinct removes duplicates from a bag. aggFun is an aggregation function (max, min, count, sum, avg) gc groups a bag of pairs on their first component and applies an aggregation function to the second component. The constructs in lines 9, ....

Albert, J.: Algebraic properties of bag data types. In: 17th International Conference on Very Large Data Bases, September 3-6, 1991.

....I(m) i, eq(i) gives all the elements m in M such that I(m) i, geq(i) gives all the elements m in M such that I(m) i, and gt(i) gives all the elements m in M such that I(m) i. See also CO, COSet, and COList. See [4] for an introduction to structural recursion as a query paradigm. See [9, 1, 6] for a description of standard bag operators. See [10] for more information on the theory of bags. See [5] for an introduction to lazy evaluation. 33 5 COBase structure COBase Routines for managing extensible base types. The user must supply a linear order for each base types added to the ....

J. Albert. Algebraic properties of bag data types. In Proceedings of 17th International Conference on Very Large Databases, pages 211-219, 1991.

....language, IQL [18] This supports a number of primitive types such as booleans, strings and numbers, as well as product, function and bag types. The set of simple IQL queries are as follows, where D, D 1 . D r denote a bag of the appropriate type, is bag union, Gamma Gamma is bag monus [1], group groups a bag of pairs on their first component, sortDistinct sorts a bag and removes duplicates, aggFun is an aggregation function (max, min, count, sum, avg) and gc groups a bag of pairs on their first component and applies an aggregation function to the second component: q = D 1 D 2 ....

J. Albert. Algebraic properties of bag data types. In Proc. VLDB'91, pages 211--219, 1991.

.... of a view V is to maintain V s data only by computing the changes to V (AV and VV) that are generated from the changes in the base relations (9i s and 7Di s) When a base relation Di has changed, we obtain the new extent of the view as V new = V AV) VV, where is the bag monus operator [Alb91]. Of course many such expressions for AV and VV are possible but not all are equally desirable. For example, we could simply let VV = Vand AV= V new, but this is equivalent to recomputing the view from scratch [Qua96] To guard against such useless definitions, it is necessary to introduce the ....

J. Albert. Algebraic properties of bag data types. In VLDB'91, pages 211-219, 1991.

....m Q makes Property 1 not to hold. Similarly manipulating the number of duplicates, we can also prove the properties 2 and 3 of the theorem. In the manipulations that follow we use the algebraic properties that appear in Table 3.1. Some of these properties are taken from the paper of Albert [Alb91] and the paper of Grumbach and Milo [GM93b] on multisets. The others can be proven easily. Chapter 3. Change Propagation Expressions 33 P 1 : A Theta (B [ C) A Theta B) A Theta C) P 2 : A Theta (B Gamma C) A Theta B) Gamma (A Theta C) P 3 : A Gamma B) Gamma C = A Gamma (B ....

J. Albert. Algebraic Properties of Bag Data Types. In 17th International Conference on Very Large Databases, pages 211--219, 1991.

....The data items, the tuples, are unordered, and the relations contain no duplicates, and cannot be nested. Relaxing these assumptions leads to numerous distinct data types, such as the complex objects (nested sets) Jac82, AB87, KV84, KRS85, AG91] the bags (sets with duplicates) BK90, Mum90, Alb91, BS91, GM93, LW94] the lists (internal order) the ordered sets, and the pomsets (partially ordered multisets) Pra84] 2.1 Partially Ordered Multisets Pomsets The pomset type generalizes sets, bags, lists, trees, and other ordered types, and therefore provides a uniform representation for ....

J. Albert. Algebraic properties of bag data types. In Proc. 17th Int'l Conf. on Very Large Data Bases, pages 211--219, 1991.

....relax this restriction [MD86, Fis87, HM81, CDV88] and support bags in their data model, often to save the cost of duplicate elimination. Efforts have been made for providing a theoretical framework for such systems. Algebras for manipulating bags were developed by extending the relational algebra [DGK82, KG85, Alb91], and optimization techniques for these algebras were studied [BK90, Mum90, Alb91] Computational aspects of bags were studied in [BS91] However, while the expressive power of database languages is of major interest in database research, the expressive power of languages for manipulating bags ....

....model, often to save the cost of duplicate elimination. Efforts have been made for providing a theoretical framework for such systems. Algebras for manipulating bags were developed by extending the relational algebra [DGK82, KG85, Alb91] and optimization techniques for these algebras were studied [BK90, Mum90, Alb91]. Computational aspects of bags were studied in [BS91] However, while the expressive power of database languages is of major interest in database research, the expressive power of languages for manipulating bags constitutes a new topic of research. On the other hand, there has been a wide ....

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J. Albert. Algebraic properties of bag data types. In Proc. 17th Int'l Conf. on Very Large Data Bases, pages 211--219, 1991.

....operation. Many theoretical results obtained for set theoretic semantics do not carry over to bags. In trying to bridge the gap between theoretical database research and practical languages, one particularly active research topic has been the design of bag languages [17, 24, 16] Bag primitives [2] formed the basis for the algebras suggested by [11, 19] These algebras turned out to be equivalent and accepted as the basic bag algebra. In this paper we use the basic bag algebra from [11, 19] It was also shown that the basic bag algebra essentially adds the correct evaluation of aggregate ....

.... It was also shown that the basic bag algebra essentially adds the correct evaluation of aggregate functions to the relational algebra, and this continues to hold when nested relations are present [20] There are a number of deep results on the complexity and expressive power of 1 bag languages [11, 2, 19, 20, 21, 22, 31]. The main goal of this paper is to lay the foundation for incremental maintenance of views defined in the bag algebra. We advocate an approach based on equational reasoning. That is, for each primitive in the bag algebra we derive an equation that shows how the result of applying this primitive ....

J. Albert. Algebraic properties of bag data types. In Proceedings of Very Large Databases--91, pages 211--219.

....Only sets have been considered in [INV91a, INV91b, LW93a, Rou91] but many practical languages are based on bags (multisets) In the past few years several approaches to design of bag languages have been proposed. Moreover, most approaches agree on what constitutes the basic set of bag operations [Alb91, GM93, LW93b, LW94]. Thus, we believe the normalization mechanism must be extended to bags. ffl Normalization may cause exponential blowup in the size of objects. For objects of size n, the size of their normal forms is bounded (roughly) by n Delta 1:45 n [LW93a] Therefore, we need better normalization tools. ....

J. Albert. Algebraic properties of bag data types. In VLDB-91, pages 211--219.

....the authors. In addition, a practical procedure is offered for determining when a type of transformation rule is applicable to a query. Finally, an algorithm is provided that generates equivalent query evaluation plans. Some work has been reported on non temporal relational algebras for multisets [Alb91, DGK82, GM00], with the most recent of these, by Garcia Molina et al. being also the most extensive. This book offers comprehensive coverage of query transformations that preserve set as well as multiset equivalences. Formalizing relations as multisets, sorting is permitted only at the outermost level. ....

....being defined as lists. The coalescing of Bohlen et al. merges value equivalent tuples with adjacent or overlapping time periods; in our algebra, this result is achieved by combining temporal duplicate elimination and coalescing. Union ( originates from the union operation for multisets given in [Alb91]. This operation includes a tuple in the result as many times as the tuple occurs in the argument relation that has the most occurrences of that tuple. Its temporal counterpart is denoted by [ T . Operation Sorting Cardinality Duplicates Coalescing Order (result) n(result) P (r) Order(r) ....

[Article contains additional citation context not shown here]

J. Albert. Algebraic Properties of Bag Data Types. In Proceedings of VLDB, Barcelona, Spain, pp. 211--219 (1991).

....transformation rules that preserve these types of equivalences and describes when a rule of some type is applicable to a query. Finally, an algorithm is provided that generates equivalent query evaluation plans. Some work has been reported on non temporal relational algebras for multisets [1, 7, 9], with the most recent of these works [9] by Garcia Molina et al. being also the most extensive. This book offers comprehensive coverage of query transformations that preserve set as well as multiset equivalences. Formalizing relations as multisets, sorting is permitted only at the outermost ....

....by superscript T . The temporal operations conceptually evaluate the result at each point of time. This is exemplified by the difference between regular and temporal duplicate elimination, to be discussed in Section 2.5. Next, union ( originates from the union operation for multisets given in [1]. This operation includes a tuple in the result as many times as the tuple occurs in the argument relation that has the most occurrences of that tuple. The temporal counterpart of union is denoted by [ T . We also add coalescing, which merges value equivalent tuples with adjacent time periods, ....

J. Albert. Algebraic Properties of Bag Data Types. In Proceedings of VLDB, Barcelona, Spain, pp. 211--219 (1991).

....languages remained open. In the past few years, several researchers explored the connection between relational languages with aggregate functions and languages whose main data structures are bags rather than sets. Among the issues that were studied are interdefinability of their primitives [4, 22, 18], complexity [18] optimization [7] equational theories [17] and, finally and most recently, the limitations of their expressive power [23, 24] In particular, it was shown in [23] that the transitive closure of a graph remains inexpressible even when grouping and aggregation are added to the ....

J. Albert. Algebraic properties of bag data types. In VLDB'91, pages 211--219.

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J. Albert. Algebraic properties of bag data types. In VLDB, 1991.

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J. Albert. Algebraic properties of bag data types. In VLDB'91, pages 211--219.

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J. Albert. Algebraic properties of bag data types. In Proceedings of 17th International Conference on Very Large Data Bases, pages 211--219, 1991.

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J. Albert, Algebraic properties of bag data types, in "Proceedings of 17th International Conference on Very Large Data Bases," 1991.

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J. Albert. Algebraic Properties of Bag Data Types. In Proceedings of VLDB, Barcelona, Spain, pp. 211--219 (1991).

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J. Albert. Algebraic Properties of Bag Data Types. In Proceedings of VLDB, Barcelona, Spain, pp. 211--219 (1991).

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Albert, J.: Algebraic properties of bag data types. In: 17th International Conference on Very Large Data Bases, September 3-6, 1991.

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J. Albert. Algebraic Properties of Bag Data Types. In Proc. VLDB, pp. 211--219 (1991).

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J. Albert. Algebraic properties of bag data types. In VLDB'91, pages 211-219, 1991.

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J. Albert. Algebraic properties of bag data types. In Proc. VLDB'91, pages 211--219, 1991.

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J. Albert. Algebraic properties of bag data types. In VLDB, 1991.

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Albert, J. Algebraic properties of bag data types, Proc. 17th VLDB, Barcelona, September 1991, pp 211-219.

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