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Approximation in Databases
 In PPCP'93, First International Workshop on Principles and Practice of Constraint Programming
, 1995
"... One source of partial information in databases is the need to combine information from several databases. Even if each database is complete for some "world", the combined databases will not be, and answers to queries against such combined databases can only be approximated. In this paper w ..."
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Cited by 141 (15 self)
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One source of partial information in databases is the need to combine information from several databases. Even if each database is complete for some "world", the combined databases will not be, and answers to queries against such combined databases can only be approximated. In this paper we describe various situations in which a precise answer cannot be obtained for a query asked against multiple databases. Based on an analysis of these situations, we propose a classification of constructs that can be used to model approximations. A major goal is to obtain universality properties for these models of approximations. Universality properties suggest syntax for languages with approximations based on the operations which are naturally associated with them. We prove universality properties for most of the approximation constructs. Then we use them to design languages built around datatypes given by the approximation constructs. A straightforward approach results in langauges that have a numb...
Temporal Query Languages: a Survey
, 1995
"... We define formal notions of temporal domain and temporal database, and use them to survey a wide spectrum of temporal query languages. We distinguish between an abstract temporal database and its concrete representations, and accordingly between abstract and concrete temporal query languages. We als ..."
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Cited by 116 (11 self)
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We define formal notions of temporal domain and temporal database, and use them to survey a wide spectrum of temporal query languages. We distinguish between an abstract temporal database and its concrete representations, and accordingly between abstract and concrete temporal query languages. We also address the issue of incomplete temporal information. 1 Introduction A temporal database is a repository of temporal information. A temporal query language is any query language for temporal databases. In this paper we propose a formal notion of temporal database and use this notion in surveying a wide spectrum of temporal query languages. The need to store temporal information arises in many computer applications. Consider, for example, records of various kinds: financial [37], personnel, medical [98], or judicial. Also, monitoring data, e.g., in telecommunications network management [4] or process control, has often a temporal dimension. There has been a lot of research in temporal dat...
The DEDALE System for Complex Spatial Queries
, 1998
"... This paper presents dedale, a spatial database system intended to overcome some limitations of current systems by providing an abstract and nonspecialized data model and query language for the representation and manipulation of spatial objects. dedale relies on a logical model based on linear const ..."
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Cited by 93 (9 self)
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This paper presents dedale, a spatial database system intended to overcome some limitations of current systems by providing an abstract and nonspecialized data model and query language for the representation and manipulation of spatial objects. dedale relies on a logical model based on linear constraints, which generalizes the constraint database model of [KKR90]. While in the classical constraint model, spatial data is always decomposed into its convex components, in dedale holes are allowed to fit the need of practical applications. The logical representation of spatial data although slightly more costly in memory, has the advantage of simplifying the algorithms. dedale relies on nested relations, in which all sorts of data (thematic, spatial, etc.) are stored in a uniform fashion. This new data model supports declarative query languages, which allow an intuitive and efficient manipulation of spatial objects. Their formal foundation constitutes a basis for practical query optimizati...
Finitely Representable Databases
, 1995
"... : We study classes of infinite but finitely representable databases based on constraints, motivated by new database applications such as geographical databases. We formally define these notions and introduce the concept of query which generalizes queries over classical relational databases. We prove ..."
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Cited by 56 (8 self)
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: We study classes of infinite but finitely representable databases based on constraints, motivated by new database applications such as geographical databases. We formally define these notions and introduce the concept of query which generalizes queries over classical relational databases. We prove that in this context the basic properties of queries (satisfiability, containment, equivalence, etc.) are nonrecursive. We investigate the theory of finitely representable models and prove that it differs strongly from both classical model theory and finite model theory. In particular, we show that most of the well known theorems of either one fail (compactness, completeness, locality, 0/1 laws, etc.). An immediate consequence is the lack of tools to consider the definability of queries in the relational calculus over finitely representable databases. We illustrate this very challenging problem through some classical examples. We then mainly concentrate on dense order databases, and exhibit...
SpatioTemporal Data Handling with Constraints
, 1998
"... Most spatial information systems are limited to a fixed dimension (generally 2) which is not extensible. On the other hand, the emerging paradigm of constraint databases allows the representation of data of arbitrary dimension, together with abstract query languages. The complexity of evaluating que ..."
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Cited by 47 (6 self)
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Most spatial information systems are limited to a fixed dimension (generally 2) which is not extensible. On the other hand, the emerging paradigm of constraint databases allows the representation of data of arbitrary dimension, together with abstract query languages. The complexity of evaluating queries though might be costly if the dimension of the objects is really arbitrary. In this paper, we present a data model, based on linear constraints, dedicated to the representation and manipulation of multidimensional data. In order to preserve a low complexity for query evaluation, we restrict the orthographic dimension of an object O, defined as the dimension of the components O1 ; :::; On such that O = O1 \Theta \Delta \Delta \Delta \Theta On . This allows to process queries independently on each component, therefore achieving a satisfying tradeoff between design simplicity, expressive power of the query language and efficiency of query evaluation. We illustrate these concepts in the co...
Topological Queries in Spatial Databases
 Journal of Computer and System Sciences
, 1996
"... We study topological queries over twodimensional spatial databases. First, we show that the topological properties of semialgebraic spatial regions can be completely specified using a classical finite structure, essentially the embedded planar graph of the region boundaries. This provides an invar ..."
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Cited by 44 (2 self)
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We study topological queries over twodimensional spatial databases. First, we show that the topological properties of semialgebraic spatial regions can be completely specified using a classical finite structure, essentially the embedded planar graph of the region boundaries. This provides an invariant characterizing semialgebraic regions up to homeomorphism. All topological queries on semialgebraic regions can be answered by queries on the invariant whose complexity is polynomially related to the original. Also, we show that for the purpose of answering topological queries, semialgebraic regions can always be represented simply as polygonal regions. We then study query languages for topological properties of twodimensional spatial databases, starting from the topological relationships between pairs of planar regions introduced by Egenhofer. We show that the closure of these relationships under appropriate logical operators yields languages which are complete for topological prope...
New Results on Quantifier Elimination Over Real Closed Fields and Applications to Constraint Databases
 Journal of the ACM
, 1999
"... In this paper we give a new algorithm for quantifier elimination in the first order theory of real closed fields that improves the complexity of the best known algorithm for this problem till now. Unlike previously known algorithms [3, 28, 22] the combinatorial part of the complexity (the part depen ..."
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Cited by 42 (5 self)
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In this paper we give a new algorithm for quantifier elimination in the first order theory of real closed fields that improves the complexity of the best known algorithm for this problem till now. Unlike previously known algorithms [3, 28, 22] the combinatorial part of the complexity (the part depending on the number of polynomials in the input) of this new algorithm is independent of the number of free variables. Moreover, under the assumption that each polynomial in the input depend only on a constant number of the free variables, the algebraic part of the complexity (the part depending on the degrees of the input polynomials) can also be made independent of the number of free variables. This new feature of our algorithm allows us to obtain a new algorithm for a variant of the quantifier elimination problem. We give an almost optimal algorithm for this new problem, which we call the uniform quantifier elimination problem. Using the uniform quantifier elimination algorithm, we give a...
Variable Independence and Aggregation Closure
 IN ACM SYMPOSIUM ON PRINCIPLES OF DATABASE SYSTEMS
, 1996
"... We discuss the issue of adding aggregation to constraint databases. Previous work has shown that, in general, adding aggregates to constraint databases results in languages that are not closed. We show that by imposing a natural restriction, called variable independence (which is a generalization of ..."
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Cited by 31 (10 self)
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We discuss the issue of adding aggregation to constraint databases. Previous work has shown that, in general, adding aggregates to constraint databases results in languages that are not closed. We show that by imposing a natural restriction, called variable independence (which is a generalization of the assumptions underlying the classical relational model of data) on the schema, we can guarantee that a restricted version of the language with aggregation is closed. We illustrate our approach in the context of linear constraint databases.
Manipulating Spatial Data in Constraint Databases
, 1997
"... . Constraint databases have recently been proposed as a powerful framework to model and retrieve spatial data. In a constraint database, a spatial object is represented as a quantifier free conjunction of (usually linear) constraints, called generalized tuple. The set of solutions of such quantifier ..."
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Cited by 29 (4 self)
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. Constraint databases have recently been proposed as a powerful framework to model and retrieve spatial data. In a constraint database, a spatial object is represented as a quantifier free conjunction of (usually linear) constraints, called generalized tuple. The set of solutions of such quantifier free formula represents the set of points belonging to the extension of the object. The relational algebra can be easily extended to deal with generalized relations. However, such algebra has some limitations when it is used for modeling spatial data. First of all, there is no explicit way to deal with the set of points representing a spatial object as a whole. Rather, only pointbased computations can be performed using this algebra. Second, practical constraint database languages typically use linear constraints. This allows to use efficient algorithms but, at the same time, some interesting queries cannot be represented (for example, the distance between two objects cannot be computed). ...
Linear constraint query languages: Expressive power and complexity
 Logic and Computational Complexity
, 1994
"... Abstract. We giveanAC 0 upper bound on the complexity of rstoder queries over (in nite) databases de ned by restricted linear constraints. This result enables us to deduce the nonexpressibility ofvarious usual queries, such as the parity of the cardinality of a set or the connectivity of a graph i ..."
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Cited by 27 (12 self)
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Abstract. We giveanAC 0 upper bound on the complexity of rstoder queries over (in nite) databases de ned by restricted linear constraints. This result enables us to deduce the nonexpressibility ofvarious usual queries, such as the parity of the cardinality of a set or the connectivity of a graph in rstorder logic with linear constraints. 1