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Probabilistic Temporal Databases, I: Algebra
"... ... In this paper, we first introduce the syntax of TemporalProbabilistic (TP) relations and then show how they can be converted to an explicit, significantly more spaceconsuming form called Annotated Relations. We then present a Theoretical Annotated Temporal Algebra (TATA). Being explicit, TATA ..."
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Cited by 33 (7 self)
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... In this paper, we first introduce the syntax of TemporalProbabilistic (TP) relations and then show how they can be converted to an explicit, significantly more spaceconsuming form called Annotated Relations. We then present a Theoretical Annotated Temporal Algebra (TATA). Being explicit, TATA is convenient for specifying how the algebraic operations should behave, but is impractical to use because annotated relations are overwhelmingly large. Next, we
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 (5 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). ...
Moving Objects: Logical Relationships and Queries, C.S. Jensen etc. : Advances in Spatial and Temporal Databases
 A Spatiotemporal Model and Language for Moving Objects on Road Networks, C.S. Jensen etc. : Advances in Spatial and Temporal Databases
, 2001
"... Abstract. In moving object databases, object locations in some multidimensional space depend on time. Previous work focuses mainly on moving object modeling (e.g., using ADTs, temporal logics) and ad hoc query optimization. In this paper we investigate logical properties of moving objects in connect ..."
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Abstract. In moving object databases, object locations in some multidimensional space depend on time. Previous work focuses mainly on moving object modeling (e.g., using ADTs, temporal logics) and ad hoc query optimization. In this paper we investigate logical properties of moving objects in connection with queries over such objects using tools from differential geometry. In an abstract model, object locations can be described as vectors of continuous functions of time. Using this conceptual model, we examine the logical relationships between moving objects, and between moving objects and (stationary) spatial objects in the database. We characterize these relationships in terms of position, velocity, and acceleration. We show that these fundamental relationships can be used to describe natural queries involving time instants and intervals. Based on this foundation, we develop a concrete data model for moving objects which is an extension of linear constraint databases. We also present a preliminary version of a logical query language for moving object databases. 1
Towards Data Mining Operators in Database Systems: Algebra and Implementation
 University of Manchester, Department of Computer Science
, 2004
"... The KDD process is a nontrivial process of identifying valid, novel, potentially useful, and ultimately understandable patterns in data. This process comprises several steps which are invoked and parametrized in an interactive and iterative manner. A uniform framework for different kinds of patt ..."
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The KDD process is a nontrivial process of identifying valid, novel, potentially useful, and ultimately understandable patterns in data. This process comprises several steps which are invoked and parametrized in an interactive and iterative manner. A uniform framework for different kinds of patterns and operators is needed to support KDD efficiently and in an integrated way. Furthermore, because of large data sets it is necessary to scale up mining algorithms in order to achieve fast user support. One task of scaling data mining algorithms is the integration of KDD operators in database management systems.
Introducing External Functions in Constraint Query Languages
, 1998
"... . Constraint databases use constraints to model and query data. In particular, constraints allow a finite representation of infinite sets of relational tuples (also called generalized tuples). The choice of different logical theories to express constraints inside relational languages leads to the de ..."
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Cited by 3 (2 self)
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. Constraint databases use constraints to model and query data. In particular, constraints allow a finite representation of infinite sets of relational tuples (also called generalized tuples). The choice of different logical theories to express constraints inside relational languages leads to the definition of constraint languages with different expressive power. Practical constraint database languages typically use linear constraints. This choice allows the use of efficient algorithms but, at the same time, some useful queries, needed by the considered application, may not be represented inside the resulting languages (for example, the convex hull cannot be computed [19]). These additional queries can only be modeled by changing the theory (thus, loosing the advantages of the linear theory), or extending the language, or using external functions. In this paper we consider the last approach and we propose an algebra and a calculus for constraint relational databases extended with exter...
Hierarchical Optimization of Linear Constraint Processing
, 2000
"... . We consider the problem of solving a large number of simple systems of constraints. This problem occurs in the context of databases with very large collections of data while the constraints are over a small number of variables. The methodology we develop is based on a hierarchical evaluation of ..."
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Cited by 2 (1 self)
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. We consider the problem of solving a large number of simple systems of constraints. This problem occurs in the context of databases with very large collections of data while the constraints are over a small number of variables. The methodology we develop is based on a hierarchical evaluation of the constraints which are first simplified, and replaced by constraints approximating the initial ones. We focus on systems of linear constraints over the reals, which model spatial objects, and consider both geometric and topological approximations, defined with very simple constraints. We show that these constraints can be used either to solve the initial systems, or at least to filter out unsatisfiable systems. More generally, we consider the manipulation of the spatial objects with firstorder queries. We show how the queries can be evaluated by taking advantage of the approximations. In general, it is undecidable if a query can be completely answered on approximated data. The ...
An Application of Advanced SpatioTemporal Formalisms to Behavioural Ecology
"... Abstract. There is great potential for the development of many new applications using data on mobile objects and mobile regions. To promote these kinds of applications advanced data management techniques for the representation and analysis of mobilityrelated data are needed. Together with applicati ..."
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Abstract. There is great potential for the development of many new applications using data on mobile objects and mobile regions. To promote these kinds of applications advanced data management techniques for the representation and analysis of mobilityrelated data are needed. Together with application experts (behavioural ecologists), we investigate how two novel data management approaches may help. We focus on a case study concerning the analysis of fauna behaviour, in particular crested porcupines, which represents a typical example of mobile object monitoring. The first technique we experiment with is a recently developed conceptual spatiotemporal data modelling approach, MADS. This is used to model the schema of the database suited to our case study. Relying on this first outcome a subset of the problem is represented in the logical language MuTACLP. This allows us to formalise and solve the queries which enable the behavioural ecologists to derive crested porcupines behaviour from the raw data on animal movements. Finally, we investigate the support from a commercial Geographical Information System (GIS) for the analysis of spatiotemporal data. We present a way to integrate MuTACLP and a GIS, combining the advantages of GIS technology and the expressive power of MuTACLP. 1
A General Strategy for Decomposing Topological Invariants of Spatial Databases and an Application
, 2001
"... Topological invariants of spatial databases (i.e., nite structures that capture the topological properties of the database) are receiving increasing attention since they can act as a basic structure to tackle relevant problems in the eld (e.g., assessment of the topological equivalence). In this p ..."
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Topological invariants of spatial databases (i.e., nite structures that capture the topological properties of the database) are receiving increasing attention since they can act as a basic structure to tackle relevant problems in the eld (e.g., assessment of the topological equivalence). In this paper, the novel notion of boundary decomposition of a topological invariant is introduced and a polynomial time algorithm to compute such a decomposition is given. The decomposition consists of a recursive subdivision of the topological invariant into a nite set of simpler structures, each being a topological invariant in itself. The decomposition is proved to be lossless, a nice property which makes the boundary decomposition useful in real applications. As a relevant application, we use the boundary decomposition as the basis for devising a polynomial time algorithm for testing the topological equivalence of two 2dimensional spatial databases.
A Relational Algebra for Functional Logic Deductive Databases
"... In this paper, we study the integration of functional logic programming and databases by presenting a data model, and a query and data definition language. The query and data definition language is based on the use of a set of algebra operators over an extended relational algebra. The algebra ex ..."
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In this paper, we study the integration of functional logic programming and databases by presenting a data model, and a query and data definition language. The query and data definition language is based on the use of a set of algebra operators over an extended relational algebra. The algebra expressions built from the extended algebra are used for expressing queries and rules. In addition, algebra expressions can be used for defining functions, typical in a functional logic program.