D.Q. Goldin and P.C. Kanellakis. Constraint Query Algebras. Constraints Journal, 1st issue (E. Freuder editor), 1--41, 1996. 104  Home/Search   Document Details and Download   Summary   Related Articles   Check

....allowing the handling of in nite relations (for instance, representing spatial and temporal data) although nitely representable, and the querying mechanism deals eciently with this nite representation. On the other hand, as in the relational database model, di erent calculi and algebras [1, 12, 19, 7] have been developed as query formalisms for these new database paradigms. These calculi and algebras extend the relational calculus and algebra, by adding the handling of complex values and constraints. In the case of complex values [1] the calculi extend the relational rst order logic, for ....

.... the case of constraint This work has been partially supported by the Spanish project INDALOG TIC200203968 databases, the calculi extend relational rst order logic, incorporating the handling of di erent classes of constraints, such as equalities and disequalities over integer and real numbers [12], linear constraints over real numbers [20] among others. Relational calculi use a fragment of the rst order logic for expressing queries against databases. The built formulas must ensure the so called domain independence property. A formula is domain independent whenever the query satis es, ....

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P. Kanellakis and D. Goldin. Constraint Query Algebras. Constraints, 1(1-2):45-83, 1996.

....constraints, respectively. In this line, we have developed syntactic conditions over our query language, which allow the building of the so called safe formulas. Extended relational calculi have been studied as alternative query languages for deductive databases [1] and constraint databases [8, 10]. Our extended relational calculus is in the line of [1] in which deductive databases handle complex values in the form of set and tuple constructors. In our case, we generalize the mentioned calculus for handling complex values built from (arbitrary) recursively de ned datatypes. In addition, ....

P. Kanellakis and D. Goldin. Constraint Query Algebras. Constraints, 1(1-2):45{ 83, 1996.

....with temporal constraints is undecidable. However, an evaluation of relational calculus queries with temporal constraints is possible and is considered by Koubarakis in [19, 20] Efficient tests for temporal constraint satisfaction are described in [9] and for monotone two variable constraints in [11]. Chomicki and Imielinski [7] consider the language Datalog 1S which is like Datalog extended with an increment operator which may occur only in the first argument of relations. Linear recursive Datalog 1S is a subcase of Datalog . The least fixpoint is evaluable for Datalog 1S queries [7] ....

D. Goldin, P.C. Kanellakis. Constraint Query Algebras. Constraints, vol. 1, no. 1&2, 54-83, 1996.

.... this sense, for example, constraints are a powerful mechanism to model spatial and temporal concepts that arise in DBs, where often infinite information has to be represented [13] To deal with constraints, both the relational calculus and the relational algebra of classical DBs have been extended [110, 111, 77], leading to new and more expressive query languages for which many properties are being studied. An example of such languages is obtained by adding linear constraints to Datalog, which has been studied in [146] Other examples are safe stratified Datalog, considered in [145] and the integration ....

D. Q. Goldin and P. Kanellakis. Constraint query algebras. CONSTRAINTS: An International Journal, 1(1 and 2):45--84, 1996.

....extensible or spatial database systems. It is also claimed, that for linear constraints, query languages manipulating constraint objects are deeply optimizable, in terms of indexing and filtering (e.g. BLLM95, KRVV93, Sri92] and constraint algebra algorithms and global optimization (e.g. BJM93, GK] More specifically, constraint algebras operate on a family F of canonical representations of constraint expressions (objects) For constraint objects C 1 ; Cn a first order logic formula OE(C 1 ; Cn ) such as 9y(C 1 [u 1 =y; v 1 =z] Cn [u n =y; v n =z] where [u i =y; v i ....

....is the development of constraint families and algebras, that strike, for each application realm, a careful balance between (1) expressiveness, 2) computational complexity and, very importantly, 3) representation usefulness. As one extreme, if the entire first order logic (as studied in [ACGK94, VGG95] and the same atomic constraints are allowed in both constraint family F and algebra, we get a very expressive algebra with low data complexity, since no actual manipulation of constraints would be required. However, the representation of the result might consist of a very large ....

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D. Q. Goldin and P.C. Kanellakis. Constraint query algebras. Constraints Journal, to appear.

....et al. 1989, Levy and Sagiv, 1992) concentrate on optimizing by repositioning constraints and assume the implementation of selection, projection and join and optimization of expressions involving these operators. Constraint algebra algorithms for specific constraint families was considered in (Goldin and Kanellakis, 1996) and constraint approximation based optimization in (Brodsky and Wang, 1995) The work (Brodsky et al. 1995) proposed an approach to achieve the optimal quality of constraint and spatial filtering. A number of works consider special constraint domains: integer order constraints (Revesz, 1993) ....

Goldin, D.Q. & Kanellakis, P.C. (1996). Constraint query algebras. Constraints, 1, 45--83, 1996.

....On the other side, we want to provide existing spatio temporal DBMS with the facility and expressiveness of a constraint based model. The recent fields of CDBs has initiated at the beginning of the decade [11] and has lead to sound data models and query languages for multi dimensional data [6, 5, 13]. The big challenge of constraint databases is to introduce constraints as basic data type in databases. The syntax is constraints, i.e. symbolic expressions; the semantics are the corresponding (possibly infinite) set of tuples that satisfy the constraint. From this data modeling perspective, ....

....(possibly infinite) set of tuples that satisfy the constraint. From this data modeling perspective, constraints are used as a unifying data type for the representation of different sorts of multi dimensional data. Most of the existing frameworks are built on the top of relational data models [6, 2] or of pure object oriented data models [7, 10] In spite of their expressiveness, the existing constraint databases are not always efficient enough for real problems where the size and the complexity of data are high. The design of our model is based on two principles. Firstly, constraints must ....

D.Q. Goldin and P.C. Kanellakis. Constraint query algebras. Constraint Journal, 1st issue, pages 45--83, 1996.

....is very attractive from a database point of view since it is completely declarative and since often constraints represent the communication language of several high level applications. During the last few years, a lot of work has been done in order to introduce constraints in both relational [16], 20] 23] 24] and object oriented databases [8] 21] In this paper, we only consider relational databases. Constraints can be added to relational database systems at different levels. At the data level, they are able to finitely represent possibly infinite sets of relational tuples. ....

....but this is not always true for calculus based languages. A. BELUSSI et al. AN EXTENDED ALGEBRA FOR CONSTRAINT DATABASES 101 algebra. In particular, the relational algebra can be easily extended to deal with generalized relations. The obtained algebra is called generalized relational algebra [16], 23] 31] The main principles underlying the algebraic approach have been discussed in [16] 23] Motivations: Among the various topics that should be investigated to make constraint databases a practical technology, we believe that there are at least two issues to consider from a modeling ....

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D.G. Goldin and P.C. Kanellakis, "Constraint Query Algebras," Constraints Journal, To appear.

....Example 9. Below we give some examples of UTVPI 6= constraints: Gammax 1 12; x 1 x 2 2; x 3 Gamma x 2 0:5; x 3 x 2 6= 6 UTVPI 6= constraints are an interesting subclass of linear constraints for spatial databases over Q 2 . They are more expressive than dense order constraints [23, 9, 10], and thus they allow more precise approximations of arbitrary regions of Q 2 traditionally approximated by bounding boxes. The disequations present in this class allowe a limited form of negative information (e.g. they can be used to remove points and straight lines from polygons) 10 The ....

....question. Can we extend the above theorem to the class of two variables per inequality or TVPI constraints (i.e. linear constraints of the form ax by c where x; y are variables and a; b are rational constants) TVPI constraints have previously been considered in several papers including [39, 18, 9, 10]. It is currently an open problem whether variable elimination for TVPI constraints can be done in PTIME. 9, 10] has considered monotone TVPI constraints (i.e. TVPI constraints of the form x by c with b 0) and showed that under a condition involving the graph representation of the ....

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D.Q. Goldin and P. Kanellakis. Constraint Query Algebras. Constraints, 1(1):45-- 83, 1997.

....Example 9. Below we give some examples of UTVPI 6= constraints: Gammax 1 12; x 1 x 2 2; x 3 Gamma x 2 0:5; x 3 x 2 6= 6 UTVPI 6= constraints are an interesting subclass of linear constraints for spatial databases over Q 2 . They are more expressive than dense order constraints [23, 9, 10], and thus they allow more precise approximations of arbitrary regions of Q 2 traditionally approximated by bounding boxes. The disequations present in this class allowe a limited form of negative information (e.g. they can be used to remove points and straight lines from polygons) 10 The ....

....question. Can we extend the above theorem to the class of two variables per inequality or TVPI constraints (i.e. linear constraints of the form ax by c where x; y are variables and a; b are rational constants) TVPI constraints have previously been considered in several papers including [39, 18, 9, 10]. It is currently an open problem whether variable elimination for TVPI constraints can be done in PTIME. 9, 10] has considered monotone TVPI constraints (i.e. TVPI constraints of the form x by c with b 0) and showed that under a condition involving the graph representation of the ....

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D.Q. Goldin. Constraint Query Algebras. PhD thesis, Dept. of Computer Science, Brown University, 1997.

....of spatial data. It allows to represent infinite relations by quantifier free formulae over some arithmetical domain, and to manipulate these relations in a symbolic way. An important feature of constraint databases is their ability to handle in a uniform way pointsets in arbitrary dimension [PVV94, GST94, GK96, KPV95, GK97]. Constraint databases can then be queried by standard means such as first order queries. Although this model meets our requirement of an abstract representation level, it does not solve the complexity issue. Indeed, although the data complexity has been shown to be tractable for reasonable ....

....t = 0 the object is at point P 0 . Then it moves from P 0 to P 3 , where it arrives a time t = 5, via P 1 (t = 1) and P 2 (t = 2) Sets of points can be manipulated via standard query languages that simulate, upon the constraints representation, the relational operations on infinite extensions [PVV94, GST94, GK96]. These languages are based on the first order theory of the reals which is known to be decidable [Tar51] There exists a symbolic algebra [GST94] over constraint representations that can be used to evaluate all first order queries. It consists of union, cross product, Theta, difference ....

D. Goldin and P. Kanellakis. Constraint Query Algebras. Constraints, 1(1/2), 1996.

....haben wir die Klasse der nebenl aufigen constraintbasierten Programmiersprachen [13] nicht erw ahnt, in denen Prozesse miteinander durch Abfragen und Einf ugen von Constraints interagieren. Constraints finden zudem nicht nur in Programmiersprachen verst arkt Anwendung, sondern auch in Datenbanken [6], wo Constraints es erm oglichen, viele (u. U. unendlich viele) Datenbankeintr age zu einem Eintrag zusammenzufassen. Dies ist vor allem bei der Speicherung von zeitlicher und r aumlicher Information von Nutzen. ....

D. Q. Goldin and P. C. Kanellakis. Constraint query algebras. Constraints Journal, 1(1+2):45--83, September 1996.

....with temporal constraints is undecidable. However, an evaluation of relational calculus queries with temporal constraints is possible and is considered by Koubarakis in [19, 20] Efficient tests for temporal constraint satisfaction are described in [9] and for monotone two variable constraints in [11]. Chomicki and Imielinski [7] consider the language Datalog 1S which is like Datalog extended with an increment operator which may occur only in the first argument of relations. Linear recursive Datalog 1S is a subcase of Datalog V A . The least fixpoint is evaluable for Datalog 1S queries [7] ....

D. Goldin, P.C. Kanellakis. Constraint Query Algebras. Constraints, vol. 1, no. 1&2, 54-83, 1996.

.... (as done typically in extensible or spatial database systems) For many useful constraint domains, query languages manipulating constraint objects are highly optimizable, in terms of indexing and filtering (e.g. 13,77,118] and constraint algebra algorithms and global optimization (e.g. [12,47]) Examples of implemented constraint databases are [49,16] While the use of constraints as data is a central feature in constraint databases, an important contribution of the field is the technology that has been developed with regard to the use of constraints for optimizing evaluation of ....

D. Q. Goldin and P.C. Kanellakis. Constraint query algebras. Constraints, 1996.

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D.Q. Goldin and P.C. Kanellakis. Constraint Query Algebras. Constraints Journal, 1st issue (E. Freuder editor), 1--41, 1996. 104

No context found.

D.Q. Goldin and P.C. Kanellakis. Constraint Query Algebras. Constraints Journal, 1(1/2), pp. 45-83, 1996.

No context found.

D.Q. Goldin and P.C. Kanellakis. Constraint Query Algebras. Constraints Journal, 1(1/2), pp. 45--83, 1996.

No context found.

D.Goldin, P.Kanellakis. Constraint Query Algebras. Constraints Journal, 1(1/2):45--83, 1996.

No context found.

D.Q. Goldin and P.C. Kanellakis. Constraint Query Algebras. Constraints Journal, 1(1/2):45-83, 1996.

No context found.

D.Q. Goldin and P.C. Kanellakis. Constraint Query Algebras. Constraints Journal, 1(1/2), pp. 45-83, 1996.

.... in spatial [BJM93, BK95, BLLM95, PVdBVG94, VGVG95] temporal [Cho94, Tom97] and spatiotemporal databases [GRS98a, GRS99] A variety of constraint languages have been proposed, including dense order constraints, linear arithmetic constraints and the most general polynomial constraints [GK96, BDLW98]. The fundamental relational query languages, relational algebra and calculus, and Datalog do not require that the relations be nite, and are thus applicable to constraint databases. Their evaluation mechanisms, however, are di erent than in relational databases because, instead of nite ....

....constraints in Z are atomic formulas of the form x c y, x d, and d x for c; d 2 Z; c 0. Constraint tuples formed from gap order constraints over variables x 1 ; x k can be represented by a directed graph on k 2 [Rev93] or equivalently by a matrix representation of such a graph [GK96]. In both cases, the representation is quadratic in k (worst case) A Gap Order Datalog query (program) is a nite set of Horn clauses with variables constrained by gap order constraints. Thus both the bottom up evaluation [Rev93] and the top down, memoing based evaluation [Tom97b] of Gap order ....

D.Q. Goldin and P.C. Kanellakis. Constraint Query Algebras. Constraints Journal, 1(1/2):45-83, 1996.

....a constraint database (CDB) KKR95] system for spatiotemporal data. Constraint databases are an extension of the relational database model, enriching both the data model and the query primitives with constraints. UMB CDB is built from the ground up in Java, using Constraint Query Algebra (CQA) [GK96] for internal query representation and evaluation. Data entry options include importing GIS data in E00 format, e.g. from Arc View or GRASS, as well as direct entry via an interactive data viewer editor. Data is displayed back to the user via the same interface; a visual display option is ....

....(logic programming) or procedural (algebraic) The original CDB theory [KKR95] is based on the declarative paradigm while the MLPQ GIS system [Rev] has a deductive front end. Our system, CDB UMB uses the procedural approach, with queries represented as expression trees in Constraint Query Algebra [GK96]. UMB CDB is designed as an experimental platform. Our approach of building a CDB around an algebra based middle layer is meant to provide a foundation for testing various implementational strategies (e.g. indexing structures such as [KRVV93] and query optimization strategies for linear ....

[Article contains additional citation context not shown here]

D.Q. Goldin and P.C. Kanellakis. Constraint Query Algebras. Constraints Journal, 1(1/2):45-83, 1996.

.... in spatial [BJM93, BK95, BLLM95, PVdBVG94, VGVG95] temporal [Cho94, Tom97] and spatiotemporal databases [GRS98a, GRS99] A variety of constraint languages have been proposed, including dense order constraints, linear arithmetic constraints and the most general polynomial constraints [GK96, BDLW98]. The fundamental relational query languages, relational algebra and calculus, and Datalog do not require that the relations be nite, and are thus applicable to constraint 1 databases. Their evaluation mechanisms, however, are di erent than in relational databases because, instead of nite ....

D.Q. Goldin and P.C. Kanellakis. Constraint Query Algebras. Constraints Journal, 1(1/2):45-83, 1996.

No context found.

D. G. Goldin and P. C. Kanellakis, "Constraint Query Algebras," Constrains J., 1(1-2): 45-83, 1996.

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P. Kanellakis and D. Goldin. Constraint Query Algebras. Constraints, 1(1-2):45{ 83, 1996.

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