G. Ozsoyoglu, Z. M. Ozsoyoglu, V. Matos, Extending relational algebra and relational calculus with set-valued attributes and aggregate functions, ACM Transactions on Database Systems 12, No. 4 (1987), 566--592.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....a test whether a relational expression introduces additional dependencies between attributes. This test can be used to achieve the same conclusions that we did in the temporal and spatiotemporal database examples in Section 7. Most of the previous work on aggregation, with the exception of [Klu82, OOM87, Kup94, CK95, GS96, BL99], has concentrated on a xed set of aggregation operators motivated by traditional database applications. Such operators are applicable to nite relations In fact, the proof is considerably more general. 28 and do not generalize to in nite ones. In [CK95] a special aggregation operator for ....

G. Ozsoyoglu, Z.M. Ozsoyoglu, and V. Matos. Extending Relational Algebra and Relational Calculus with Set-Valued Attributes and Aggregate Functions. ACM Transactions on Database Systems, 12:566-592, 1987.

....data model for statistical databases is introduced. The model is based on summary tables and operators defined on them such as construction destruction, concatenation extraction, attribute splitting merging and aggregation operators. The underlying algebra is a subset of the algebra described in [15]. Furthermore, physical organization and implementation issues are discussed. 14] is very close to practical OLAP operations, although discussed in the context of summary tables. In [16] a functional model CMefisto ) is presented. Mefisto is based on the definition of a data structure, called ....

....a dimension level DLi. Let V be the space of all values. A dimension level is atomic if its domain is a subset of V. If the domain of a dimension level is a subset of P(V) the power set of V) then the dimension level is multi valued. We use bag semantics for multi valued dimension levels. As in [15], we use the prefix for multi valued attributes. A value x, can have ancestors and descendants . Let x belong to a specific dimension level Lo; then, there are specific instances related to x, at higher (lower) dimension levels, corresponding to more general (detailed) terms, that is ....

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G. Ozsoyoglu, M. Ozsoyoglu, V. Matos, "Extending Relational Algebra and Relational Calculus with Set-Valued Attributes and Aggregation Functions", ACM TODS 12(4), 1987.

....a test whether a relational expression introduces additional dependencies between attributes. This test can be used to achieve the same conclusions that we did in the temporal and spatiotemporal database examples in Section 7. Most of the previous work on aggregation, with the exception of [Klu82, OOM87, Kup94, CK95, GS96, BL99], has concentrated on a xed set of aggregation operators motivated by traditional database applications. Such operators are applicable to nite relations and do not generalize to in nite ones. In [CK95] a special aggregation operator for generalized relations that preserved closure of relational ....

G. Ozsoyoglu, Z.M. Ozsoyoglu, and V. Matos. Extending Relational Algebra and Relational Calculus with Set-Valued Attributes and Aggregate Functions. ACM Transactions on Database Systems, 12:566-592, 1987. 25

....relations [Ozy87] Ozy89] Significant progress has been made in the field of nested relations during the past decade. A generalization of the ordinary relational model, allowing relations with set valued attributes and adding two restructuring operators, nest and unnest, was introduced [Jae82][OOM87]. Fisher and Van Gucht [Fis85] discussed one level nested relations and their characterization by a new family of dependencies, and furthermore, they developed a polynomial time algorithm to test if a structure is a one level nested relation. Thomas and Fischer generalized their work on the ....

G. Ozsoyoglu, Z. M. Ozsoyoglu, V. Matos. Extending relational algebra and relational calculus with set-valued attributes and aggregate functions. ACM Transaction on Database Systems, 12(4) Dec. 1987, pp. 566-593

....to this capability, perhaps because it does not seem to affect the expressive power and complexity of queries in an essential way. One exception is the work of Klug [Klu82] who formalized extensions of relational algebra and calculus with aggregates and showed their equivalence. Ozsoyoglu et al. [OOM87] extended aggregate functions to relations with set valued attributes. Both Cooper [Coo80] and Sheng [She90] have been concerned with the relative power of different aggregate operators added to the same language. More recently, Mumick et al. MPR90] Ganguly et al. GGZ91, GZG92] Lefebvre ....

G. Ozsoyoglu, Z.M. Ozsoyoglu, and V. Matos. Extending relational algebra and relational calculus with set-valued attributes and aggregate functions. ACM Transactions on Data Base Systems, 12(4):566--592, 1987.

....present framework. Finally, the proposed formalism is shown to be useful for statistical database schema design. 1. Introduction The manipulation of aggregate data raises important and specific issues, that have been studied with different foci both in the field of statistical databases (SDBs) [Sho82, Su83, SW85, Gho86, OOM87, CDL95, RBT96], and in the field of on line analytical processing (OLAP) GBLP96, HRU96, LS97, Sho97, CD97] The real challenge of this sort of data is caused by the rather intricate semantics of summary values, that is not handled by classical database systems. The relationships between OLAP and data mining ....

G. Ozsoyoglu, Z.M. Ozsoyoglu, and V. Matos. Extending relational algebra and relational calculus with set-valued attributes and aggregate functions. ACM Transactions on Database Systems, 12(4):566--592, December 1987.

....involve aggregation over evolving data of very large size. The use of materialized aggregate views, might strongly increase the efficiency of query processing. The modeling and the manipulation of statistical data have been studied with different focus both in the field of statistical databases [Su83, SW85, OOM87, Gho86, RR93, RBT96], and in the field of on line analytical processing (OLAP) GBLP96, HRU96, LS97, Sho97] The real challenge of this sort of data is caused by the rather intricate semantics of summary values, that is not handled by classical database systems. A fundamental problem of statistical databases, is to ....

G. Ozsoyoglu, Z.M. Ozsoyoglu, and V. Matos. Extending relational algebra and relational calculus with setvalued attributes and aggregate functions. ACM Transactions on Database Systems, 12(4):566--592, December 1987.

....and modifications of containment algorithms to consider semantics of class hierarchies were considered in [Cha92, LR96] However, containment and equivalence for query languages for complex objects have not been considered previously. Complex Objects Several query formalisms have been proposed [TF86, OOM87, Col93, BNTW95, AB95]. We consider the containment and equivalence problems for a certain subset of the Object Query Language, OQL [Cat94] which we call conjunctive idealized OQL, COQL. It is a generalization of conjunctive queries [Ull89] and also corresponds to natural fragments of other query languages for complex ....

....by the application of complex objects constructors. It coincides with order relations previously considered in conjunction with partial informations [BOJ91] and or sets [LW93] Containment and Equivalence of Queries with Aggregates Complex objects and aggregates are related in a natural way [OOM87]. We show how to derive from our results for complex objects new containment and equivalence results for queries with grouping and aggregation over flat relations. In particular, we show that containment is decidable for queries with arbitrary nesting of aggregation with uninterpreted aggregate ....

G. Ozsoyoglu, Z. M. Ozsoyoglu, and V. Matos. Extending relational algebra and relational calculus with set-valued attributes and aggregate functions. ACM Transactions on Database Systems, 12(4):566--592, December 1987.

.... Query 5: What is the average salary each employee earned TAE: unpack Employee on Salary) E# avg(Salary) 3 Implementation of TDBMS TDBMS has been implemented on top of ERAM [6] a database management system which is based on the extended relational model and extended relational algebra [13, 14]. The extended relational model allows relations with set valued attributes where there is only one level of nesting. It has specifically been formulated for statistical databases, and hence includes powerful aggregation features. The extended relational algebra includes the five basic operations ....

Ozsoyoglu, G., Ozsoyoglu, Z.M., Matos, V., "Extending Relational Algebra and Relational Calculus with Set-Valued Attributes and Aggregate Functions", ACM Trans. Database Syst., Vol.12, No.4, Dec. 1987, pp 566-592.

....generally a rather expensive 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 ....

G. Ozsoyoglu, Z. M. Ozsoyoglu, and V. Matos. Extending relational algebra and relational calculus with setvalued attributes and aggregate functions. ACM Transactions on Database Systems, 12 (1987), 566--592.

....to analyze expressive power of SQL like languages. Languages like SQL differ from the relational calculus in that they have grouping constructs (modeled by the SQL GROUPBY) and aggregate functions such as COUNT and AVG. After some initial investigation of extended relational languages was done in [21, 25], first results on expressive power appeared in [8] However, the results of [8] were based on the assumption that the deterministic and nondeterministic logspace are different, and thus questions on expressive power of SQL like languages remained open. In the past few years, several researchers ....

G. Ozsoyoglu, Z. M. Ozsoyoglu, V. Matos, Extending relational algebra and relational calculus with set-valued attributes and aggregate functions, ACM Transactions on Database Systems 12, No. 4 (1987), 566--592.

....data. In spite of this fact, a systematic study of aggregations in the context of query languages has evolved quite slowly. Apart from the work by Klug [13] who formalized extensions of algebra and calculus with aggregates, in the last decade there have been few papers dealing with this subject [7, 14 16], even if specific aggregate functions of theoretical relevance, like counters, have received special attention [2, 8, 11] The general approach to the problem is to study basic properties of formal languages equipped with a specific class of built in aggregate functions (typically the ones ....

G. Ozsoyoglu, Z. M. Ozsoyoglu, V. Matos. Extending relational algebra and relational calculus with set-valued attributes and aggregate functions. ACM Transactions on Database Systems, 12(4):566--592, 1987.

....can also be unnested losslessly) Investigations concerning the completeness of such languages have been presented in [127, 84] where it was shown that such an algebra is BP complete . Deeply nested algebras, that is, those that allow operations on the attribute level have been proposed in [97, 4, 58, 98, 40, 81, 93, 3, 28, 126]. Some of them require the relations to be in partitioned normal form. The algebras of [93, 28] provide operators, such as the set operators, union and difference, that apply recursively to all subrelations, therefore they need the PNF restriction. The other algebras provide explicit nesting of ....

G. Ozsoyoglu, Z. M. Ozsoyoglu, and V. Matos. Extending relational algebra and relational calculus with set-valued attributes and aggregate functions. ACM Transactions on Database Systems, 12(4):566--592, December 1987.

....means of logic; 3) the language is equipped with specialized inference procedures, allowing for performing different kinds of checks on the representation. 1 Introduction In the recent years, several approaches have been proposed for modelling large amounts of data from a statistical point of view [BD88,SW85,Su83,Gh86,OO85,OOM87]. A common characteristic of such approaches is to model elementary data by usual data models, then defining particular representation structures for summary data (i.e. data obtained by grouping elementary data, and by applying statistical operators such as total, average, percentage to such ....

Ozsoyoglu G., Ozsoyoglu Z.M., Matos V., "Extending Relational Algebra and Relational Calculus with Set-Valued Attributes and Aggregate Functions", ACM Transactions on Database Systems, 12(4): 566-592, 1987.

....programming language such as Lisp [1] where eval is clearly definable in Lisp without eval and thus not primitive. Also the other operators of MA are shown to be primitive. 1 Generalizations of Codd s theorem to extensions of the relation model have always been a popular research topic (e.g. [13, 15, 2, 11, 5]) 2 Analogous conservative extension properties are known for complex object databases [17, 26, 23] and spatial databases [16] The present paper is a follow up on an earlier paper by three of us [25] There, we studied the expressive power of evaluating stored relational algebra programs in ....

G. Ozsoyoglu, Z.M. Ozsoyoglu, and V. Matos. Extending relational algebra and relational calculus with set-valued attributes and aggregate functions. ACM Transactions on Database Systems, 12(4):566--592, 1987.

....knowledge since SQL was first conceived, little effort has been devoted to understand the connection between aggregate operators and bag query languages. Adding aggregate operations to the relational algebra was considered by Klug [30] and then extended to complex objects in Ozsoyoglu et al. [43]. The approach adopted in these papers is the following. An aggregate function is introduced separately for each column. That is, there are functions AVG 1 , AVG 2 , etc. To compute the average of the B column, one would write AVG B (R) While this approach incorporates aggregate functions into ....

G. Ozsoyoglu, Z. M. Ozsoyoglu, V. Matos, Extending relational algebra and relational calculus with set-valued attributes and aggregate functions, ACM Transactions on Database Systems 12, No. 4 (1987), 566--592.

....to analyze expressive power of SQL like languages. Languages like SQL differ from the relational calculus in that they have grouping constructs (modeled by the SQL GROUPBY) and aggregate functions such as COUNT and AVG. After some initial investigation of extended relational languages was done in [29, 40], first results on expressive power appeared in [7] However, the results of [7] were based on the assumption that the deterministic and nondeterministic logspace are different, and thus questions on the expressive power of SQL like languages remained open. In the past few years, an intimate ....

G. Ozsoyoglu, Z. M. Ozsoyoglu, V. Matos, Extending relational algebra and relational calculus with set-valued attributes and aggregate functions, ACM Transactions on Database Systems 12(4):566--592, 1987.

....on Database Systems, 12(1) 111 136, 1987. 2 nesting) and extend the basic algebra for such relations by aggregation operators. A relational calculus for set valued relations with aggregate functions is given, and its equivalence to the corresponding relational algebra is shown in [OzOM]. A relational calculus for non first normal form relations is given by Roth, Korth and Silberschatz [RKS] who also define a basic relational algebra for non first normal form relations, and show its equivalence to the relational calculus. In this paper, we introduce a normal form for nested ....

Ozsoyoglu, G., Matos, V., and Ozsoyoglu, Z.M., Extending Relational Algebra and Relational Calculus with Set-Valued Attributes and Aggregate Functions, Technical Report, Department of Computer Science, Case Western Reserve University, 1985.

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G. Ozsoyoglu, Z. M. Ozsoyoglu, V. Matos, Extending relational algebra and relational calculus with set-valued attributes and aggregate functions, ACM Transactions on Database Systems 12, No. 4 (1987), 566--592.

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G. Ozsoyoglu, Z. M. Ozsoyoglu, V. Matos, Extending relational algebra and relational calculus with set-valued attributes and aggregate functions, ACM Transactions on Database Systems 12(4):566--592, 1987.

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G. Ozsoyoglu, Z. M. Ozsoyoglu, V. Matos, Extending relational algebra and relational calculus with set-valued attributes and aggregate functions, ACM Transactions on Database Systems 12, No. 4 (1987), 566--592.

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G. Ozsoyoglu, Z.M. Ozsoyoglu, and V. Matos. Extending Relational Algebra and Relational Calculus with Set-Valued Attributes and Aggregate Functions. ACM Transactions on Database Systems, 12:566-592, 1987.

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)  Ozsoyoglu,G.,  Ozsoyoglu, Z., and Matos, V. Extending Relational Algebra and Relational Calculus with Set Valued Attributes and Aggregate Functions. In Transactions on Database Systems, 12(4):566-592, 1987.

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G. Ozsoyoglu, Z. Ozsoyoglu, and V. Matos. Extending relational algebra and relational calculus with set-valued attributes and aggregate functions. ACM Transactions on Database Systems, 12(4):566--592, December 1987.

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G. # Ozsoyoglu, Z. M. # Ozsoyoglu, V. Matos. Extending relational algebra and relational calculus with set-valued attributes and aggregate functions. ACM Transactions on Database Systems, 12#4#:566#592, 1987.

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