Leonidas Fegaras and David Maier. Towards an e#ective calculus for object query languages. In Proceedings of SIGMOD '95, San Jose, CA, pages 47--58, 1995.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....# [ # ] An operation often required when manipulating features is to determine whether a given property is verified for a given shape in any position of the array. This can be done using the sweep function, whose semantics can be defined for two dimensional arrays using monoid comprehension [2] as #(F (e) A, P ) or P (F (e) j) A) j # [0, 0] dim 1 (A) dim 2 (A) 3) The definition can be easily extended to n dimensional arrays. Other operations can be defined in a similar way simply changing the target monoid. For instance, a selection operation, which returns all the ....

....database. Second, by exposing the internal structure and the semantics of the operations, we create numerous possibilities for query optimization. Techniques for program normalization and query optimization based on the monoid comprehension calculus have been studied for quite some time [2], and our wavelet feature definition fits nicely in this framework. ....

Leonidas Fegaras and David Maier. Towards an e#ective calculus for object query languages. In Proceedings of SIGMOD '95, San Jose, CA, pages 47--58, 1995.

....of the relational model [Cod72] the introduction of the relational algebra, and the proof of its equivalence to tupleoriented relational calculus [Cod70] There has also been a lot of work on algebras in the context of object oriented databases. Our work has been influenced mostly by [FM95a] and [FM95b] Monoid homomorphisms are a strong candidate for an XML calculus that we plan to devise in our future work (see Section 9) The object oriented algebra presented in [BMG93] uses a combination of materialize and unnest to access set valued attributes which is close to what our Follow operator ....

Leonidas Fegaras and David Maier. Towards an e#ective calculus for object query languages. In Michael J. Carey and Donovan A. Schneider, editors, Proceedings of the 1995 ACM SIGMOD International Conference on Management of Data, San Jose, California, May 22-25, 1995, pages 47--58. ACM Press, 1995.

....these with work by other researchers. Section 6 concludes and points to future work. 2. TECHNICAL BACKGROUND This section introduces examples of ODL and OQL material used in the paper and brie y describes the query processing notions used in the solution, speci cally those implemented in OPTGEN [7, 8] and DB [9] The ODMG standard for object databases [5] includes an object de nition language (ODL) and an object query language (OQL) Some familiarity with this model is assumed in the paper. ODL is used to declare a schema which de nes the valid application types. Figure 1 is an example ....

....struct(E:e.name, D:d.name) from e in Employees, d in Departments where e.dept = d; define worksFor( as select struct(E:e.name, D:d.name) from e in Employees, d in Departments where e. dept = d; Figure 2: OQL Query and View The DB system [9] implements a monoid comprehension calculus [8] and a monoid algebra over the ODMG object model (not including arrays and dictionaries) OQL queries in DB are rst translated into expressions in the calculus, normalized and then translated into monoid algebraic expressions. These can be optimized before they are mapped to physical execution ....

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L. Fegaras and D. Maier. Towards an Eective Calculus for Object Query Languages. In Proc. SIGMOD, pages 47-58, 1995.

....is monoidal if every aggregate in it is. 2 The usual aggregates P and Q are monoidal, given by hQ ; 0i and hQ ; 1i respectively. In fact, most aggregates in the database setting are either monoidal or can be obtained from monoidal aggregates by means of simple arithmetic operations [9]. We now have to say what it means for a logic to capture a query language. In one direction, it is easy every query must be de nable by a logical formula. For the other direction, one has to deal with the standard database problem of safety [1] while queries always return nite results, ....

L. Fegaras and D. Maier. Towards an eective calculus for object query languages. In ACM SIGMOD'95, pages 47-58.

....one experiment each for index introduction and join elimination, both with queries and schemas of lesser complexity than what we have considered. 7] reports on join elimination in star queries that are still less complex than our experiments with EC2. Examples of SQO for OO systems appear in [28, 10, 9, 3, 14, 13, 17, 8] Use of referential integrity constraints to eliminate dependent joins is implicit in [19, 10, 20, 21] A general framework for SQO using rewrite rules expressed using OQL appears in [16, 15] Techniques for using materialized views in query optimization are discussed in [33, 31, 6, 15, 16, 30, ....

Leonidas Fegaras and David Maier. Towards an eective calculus for object query languages. In Proceedings of ACM SIGMOD International Conference on Management of Data, pages 47-58, San Jose, California, May 1995.

....OODB languages and is easy to put into canonical form, while the algebra is lower level and can be directly translated into the execution algorithms supported by database systems. Optimizing Object Queries Using an E ective Calculus 3 Our calculus is called the monoid comprehension calculus [Fegaras and Maier 1995]. As we will demonstrate in this paper, our calculus captures most features of OQL and is a good basis for expressing various optimization algorithms concisely. It is based on monoids, a general template for a data type, which can capture most collection and aggregate operators currently in use ....

....are constructed in random fashion by specifying which value is stored at what place. But there is a problem here: what if we have two di erent values stored in the same place in a vector We need to perform a merge operation on vectors. One solution is to merge the vector elements individually [Fegaras and Maier 1995]. That is, when two elements are stored at the same place in a vector, the resulting vector value is computed by merging these two elements. Another solution, which we adopt here, is to choose the latter of the two values if this value is not null, otherwise to choose the rst. That way, the last ....

Fegaras, L. and Maier, D. 1995. Towards an Eective Calculus for Object Query Languages. In ACM SIGMOD International Conference on Management of Data, San Jose, California (May 1995), pp. 47-58.

....for object oriented and object relational databases, such as query nesting, multiple collection types, methods, and arbitrary nesting of collections. We have already developed a theoretical framework for query optimization based on an e ective calculus, called the monoid comprehension calculus [4]. The system reported here is a fully operational ODMG 2.0 [2] OODB management system, based on this framework. Our system can handle most ODL declarations and can process most OQL query forms. DB is not ODMG compliant. Instead it supports its own C binding that provides a seamless integration ....

....compiler ODL C compiler evaluation engine catalog manager result formatter formulation SHORE Figure 1: DB Architecture and the VOODOO Interface intermediate code into C code, or interpretation of the intermediate code. Our calculus is called the monoid comprehension calculus [4]. It captures most features of OQL and is a good basis for expressing various optimization algorithms concisely. It is based on monoids, a general template for a data type, which can capture most collection and aggregate operators currently in use for relational and object oriented databases. One ....

L. Fegaras and D. Maier. Towards an Eective Calculus for Object Query Languages. SIGMOD'95, pp 47-58. 4

....forms because the calculus closely resembles current OODB languages and is easy to put into canonical form, while the algebra is lower level and can be directly translated into the execution algorithms supported by database systems. Our calculus is called the monoid comprehension calculus [FM95] As we will demonstrate in this paper, our calculus captures most features of OQL and is a good basis for expressing various optimization algorithms concisely. It is based on monoids, a general template for a data type, which can capture most collection and aggregate operators currently in use ....

....are constructed in random fashion by specifying which value is stored at what place. But there is a problem here: what if we have two di erent values stored in the same place in a vector We need to perform a merge operation on vectors. One solution is to merge the vector elements individually [FM95] That is, when two elements are stored at the same place in a vector, the resulting vector value is computed by merging these two elements. Another solution, which we adopt here, is to choose the last of the two values if this value is not null, otherwise to choose the rst. That way, the last ....

L. Fegaras and D. Maier. Towards an Eective Calculus for Object Query Languages. ACM SIGMOD International Conference on Management of Data, San Jose, California, pages 47-58, May 1995.

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Leonidas Fegaras and David Maier. Towards an e#ective calculus for object query languages. In Proceedings of ACM SIGMOD International Conference on Management of Data, pages 47#58, San Jose, California, May 1995.

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