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## Spatio-Temporal Data Types: An Approach to Modeling and Querying Moving Objects in Databases (1999)

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Citation Context ...tting a curve at the boundaries of a time interval.sSPATIO-TEMPORAL DATA TYPES 289 3.6. Relationship with the constraint database approach Following the seminal paper by Kanellakis, Kuper, and Revesz =-=[23]-=-, [24], the constraint database approach has gained a lot of interest, especially as a theoretically well-founded basis for spatial modeling and querying. The basic idea is that a spatial object is a,... |

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Citation Context ... databases, tuples are extended with time stamps that associate either a valid time interval (historical databases) or a transaction time interval (rollback databases), or both (bitemporal databases) =-=[32]-=-, [33]. A valid time interval expresses when this fact was true in the real world; a transaction time interval shows when the fact was believed in the database. Hence we get, for example, relations li... |

301 | Modeling and querying moving objects.
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Citation Context ...on of faces. While there are some similar ideas, they have no notion of abstract spatio-temporal data types with operations. An interesting proposal that directly addresses moving objects is given in =-=[37]-=-. Here a moving object, e.g., a car or plane, is described by a so-called dynamic attribute. A dynamic attribute contains a motion vector and can describe the current status of a moving object (e.g., ... |

214 | An introduction to spatial database systems
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Citation Context ... data models and database systems has mostly been done independently. Spatial database research has focused on supporting the modeling and querying of geometries associated with objects in a database =-=[Gü94]-=-. Temporal databases have focused on extending the knowledge kept in a database about the current state of the real world to include the past, in the two senses of “the past of the real world” (valid ... |

150 | A taxonomy of time databases
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Citation Context ...ases, tuples are extended with time stamps that associate either a valid time interval (historical databases) or a transaction time interval (rollback databases), or both (bitemporal databases) [32], =-=[33]-=-. A valid time interval expresses when this fact was true in the real world; a transaction time interval shows when the fact was believed in the database. Hence we get, for example, relations like the... |

139 |
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Citation Context ...perators. So the carrier set for a type t contains the possible values for t, and the functions are mappings between the carrier sets. For a formal definition of many-sorted signature and algebra see =-=[EM85]-=- or [Gü93]. Now it is important to understand that one can make such designs at two different levels of abstraction, namely as abstract or as discrete models. 3.3.1 Abstract Models Are Simple … Abstra... |

132 |
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Citation Context ...ral databases proposing attribute time stamps, that is, describe the development of an attribute value by giving a set of (time-interval, value) pairs, or a sequence of (time, value) pairs [6], [21], =-=[11]-=-. In fact, at an abstract level these approaches view attribute values as functions from time into some domain, as we do here. Hence this is not so far from our proposal of spatio-temporal data types.... |

107 |
An event-based spatiotemporal data model (ESTDM) for temporal analysis of geographical data:
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Citation Context ...mporal complexes. Their spatial features are given by simplicial complexes; their temporal features are described by bitemporal elements attached to all components of simplicial complexes. In [8] and =-=[27]-=- event-based approaches for ST databases are proposed. Events indicate changes of the locations and shapes of spatial objects and trigger the creation of new versions in the database. All these approa... |

98 |
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Citation Context ...d, and the spatial dimension expresses where it is valid. While each value has always a temporal evolution, it is doubtful whether it always has a spatial aspect, as discussed in Section 3.1. Worboys =-=[41]-=- de®nes spatio-temporal objects as so-called spatio-bitemporal complexes. Their spatial features are given by simplicial complexes; their temporal features are described by bitemporal elements attache... |

96 |
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Citation Context ...ese approaches view attribute values as functions from time into some domain, as we do here. Hence this is not so far from our proposal of spatio-temporal data types. Also the time sequences approach =-=[35]-=- appears much more closely related than tuple time stamps.sSPATIO-TEMPORAL DATA TYPES 279 3.2. Why not just use ``temporal databases with spatial data types'' Here the idea is quite simple: take any t... |

90 | The DEDALE System for Complex Spatial Queries
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Citation Context ... databases manipulations are restricted to what the given formalism offers (e.g., linear calculus or algebra in [39]). For example, one cannot express distance computations or connectivity predicates =-=[18]-=-. But then, one has a clear picture of the expressive power of this language. Another aspect is that users would like to formulate queries in terms of simple, natural concepts and relationships such a... |

90 | Towards a theory of spatial database queries
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Citation Context ...a ``classical'' tuple name ˆ ``Smith''6age ˆ 32, describing a single point. Various classes of constraints with different expressive power have been studied, for example, polynomial constraints [24], =-=[29]-=- or linear (polynomial) constraints (e.g., [39], [19], [3]). Note that with linear constraints, each constraint represents a hyperplane ( ˆ ) or halfspace (>, ,<, ); a conjunction of constraints can r... |

76 | The Historical Relational Data Model (HRDM) and Algebra Based on Lifespans
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Citation Context ...rk in temporal databases proposing attribute time stamps, that is, describe the development of an attribute value by giving a set of (time-interval, value) pairs, or a sequence of (time, value) pairs =-=[6]-=-, [21], [11]. In fact, at an abstract level these approaches view attribute values as functions from time into some domain, as we do here. Hence this is not so far from our proposal of spatio-temporal... |

66 |
Spatio-temporal composition and indexing large multimedia applications
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Citation Context ...wise changing region values [22], [30], [31], [5]. The general idea is to use a start version and then record the changes. Some work addresses spatio-temporal modeling within multimedia documents. In =-=[40]-=- the assumption is that objects are rectangles that appear for some time related spatially and/or temporally with other objects. The temporal relationships are represented by a set of operators that a... |

60 | Constraint-based interoperability of spatiotemporal databases
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Citation Context ...bases generally applies to spatio-temporal settings as arbitrary shapes in multidimensional spaces can be described. Two papers that explicitly deal with spatio-temporal examples and models are [18], =-=[7]-=-. Several papers in the GIS literature study storage schemes for stepwise changing region values [22], [30], [31], [5]. The general idea is to use a start version and then record the changes. Some wor... |

58 | A.: ‘Thematic Map Modelling
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Citation Context ...ection of object classes; objects may or may not have attributes of spatial data types. Research has then tried to identify ``good'' designs of collections of types and operations, or algebras (e.g., =-=[36]-=-, [34], [20]). As far as the DBMS is concerned, spatial data types are in principle not different from other data types. Of course, they need special support in indexing, join methods, etc., but this ... |

57 |
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Citation Context ...tio-bitemporal complexes. Their spatial features are given by simplicial complexes; their temporal features are described by bitemporal elements attached to all components of simplicial complexes. In =-=[8]-=- and [27] event-based approaches for ST databases are proposed. Events indicate changes of the locations and shapes of spatial objects and trigger the creation of new versions in the database. All the... |

55 | Voronoi diagrams of moving points
- Albers, Guibas, et al.
- 1998
(Show Context)
Citation Context ...he evolvement of relationships between objects. It also does not address changes in the shape of objects. Computational geometry has also shown interest in time-varying spatial objects. For instance, =-=[1]-=-, [10], [16] deal with Voronoi diagrams of moving points. The task is to maintain the Voronoi diagram when a set of points is moving continuously over time. 5. Conclusions and future work We have prop... |

51 | Realm-Based Spatial Data Types
- Güting, Schneider
- 1995
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Citation Context ...ject classes; objects may or may not have attributes of spatial data types. Research has then tried to identify ``good'' designs of collections of types and operations, or algebras (e.g., [36], [34], =-=[20]-=-). As far as the DBMS is concerned, spatial data types are in principle not different from other data types. Of course, they need special support in indexing, join methods, etc., but this might also h... |

47 |
A Query Language for a Homogeneous Temporal Database
- Gadia, Vaishnav
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Citation Context ... temporal databases proposing attribute time stamps, that is, describe the development of an attribute value by giving a set of (time-interval, value) pairs, or a sequence of (time, value) pairs [6], =-=[21]-=-, [11]. In fact, at an abstract level these approaches view attribute values as functions from time into some domain, as we do here. Hence this is not so far from our proposal of spatio-temporal data ... |

43 |
Geo-SAL—a query language for spatial data analysis
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Citation Context ... of object classes; objects may or may not have attributes of spatial data types. Research has then tried to identify ``good'' designs of collections of types and operations, or algebras (e.g., [36], =-=[34]-=-, [20]). As far as the DBMS is concerned, spatial data types are in principle not different from other data types. Of course, they need special support in indexing, join methods, etc., but this might ... |

39 | Implementation of the ROSE algebra: Efficient algorithms for realm-basedspatial data types - Güting, Ridder, et al. - 1995 |

37 | Second-order signature: a tool for specifying data models, query processing and optimization
- Güting
- 1993
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Citation Context ...So the carrier set for a type t contains the possible values for t, and the functions are mappings between the carrier sets. For a formal definition of many-sorted signature and algebra see [EM85] or =-=[Gü93]-=-. Now it is important to understand that one can make such designs at two different levels of abstraction, namely as abstract or as discrete models. 3.3.1 Abstract Models Are Simple … Abstract models ... |

35 |
An Introduction to Spatial Database Systems.
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Citation Context ... data models and database systems has mostly been done independently. Spatial database research has focused on supporting the modeling and querying of geometries associated with objects in a database =-=[13]-=-. Temporal databases have focused on extending the knowledge kept in a database about the current state of the real world to include the past, in the two senses of ``the past of the real world'' (vali... |

31 |
Bibliography on spatiotemporal databases:
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Citation Context ...cognized the need of a simultaneous treatment and integration of data with spatial and temporal features in databases. A comprehensive bibliography on spatio-temporal databases until 1994 is given in =-=[2]-=-. Many of its articles document the interaction of space and time through application examples. But nevertheless, up to now research on models for spatio-temporal databases is still in its infancy. Mo... |

29 | Manipulating Spatial Data in Constraint Databases
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Citation Context ... a single point. Various classes of constraints with different expressive power have been studied, for example, polynomial constraints [24], [29] or linear (polynomial) constraints (e.g., [39], [19], =-=[3]-=-). Note that with linear constraints, each constraint represents a hyperplane ( ˆ ) or halfspace (>, ,<, ); a conjunction of constraints can represent a point, part of a hyperplane, or a convex polyto... |

29 |
Seamless Integration of Time into SQL
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Citation Context ...ention them in a query, the behavior should be consistent with that of a standard database (these issues are known as upward compatibility, snapshot reducibility, support of legacy applications, etc. =-=[4]-=-). Because a user does not declare and see explicit time attributes, there is no big incentive to offer e.g., time intervals with a number of operations in the style of abstract data types that would ... |

26 | Cambray, Modeling Highly Variable Spatio-Temporal Data
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Citation Context ... database. All these approaches are only capable of modeling discrete or stepwise constant but not continuous temporal evolutions of spatial data.sSPATIO-TEMPORAL DATA TYPES 291 Yeh and Cambray [42], =-=[43]-=- emphasize some aspects also mentioned in our paper. Since spatial data over time can be highly variable, they consider a continuous view of these data as indispensable and a snapshot view as inapprop... |

25 | Voronoi diagrams of moving points in the plane - Fu, Lee - 1991 |

24 |
The Interval-extended Relational Model and Its Application to Valid-time Databases
- Lorentzos
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Citation Context ...ve to offer e.g., time intervals with a number of operations in the style of abstract data types that would then be used like other data types in querying (although some work in this direction exists =-=[25]-=-). Rather, special query language extensions are provided to allow the user to refer to and describe relationships between the implicit time attributes. If we try to extend this approach in a straight... |

24 |
Cambray, Time as a Geometric Dimension for Modeling the Evolution of Entities: A
- Yeh, de
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Citation Context ...in the database. All these approaches are only capable of modeling discrete or stepwise constant but not continuous temporal evolutions of spatial data.sSPATIO-TEMPORAL DATA TYPES 291 Yeh and Cambray =-=[42]-=-, [43] emphasize some aspects also mentioned in our paper. Since spatial data over time can be highly variable, they consider a continuous view of these data as indispensable and a snapshot view as in... |

22 |
Relational Spatial Topologies for Historical Geographical Information
- Raafat, Yang, et al.
- 1994
(Show Context)
Citation Context ...bed. Two papers that explicitly deal with spatio-temporal examples and models are [18], [7]. Several papers in the GIS literature study storage schemes for stepwise changing region values [22], [30], =-=[31]-=-, [5]. The general idea is to use a start version and then record the changes. Some work addresses spatio-temporal modeling within multimedia documents. In [40] the assumption is that objects are rect... |

17 | DEDALE, A spatial constraint database
- Grumbach, Rigaux, et al.
- 1997
(Show Context)
Citation Context ...ribing a single point. Various classes of constraints with different expressive power have been studied, for example, polynomial constraints [24], [29] or linear (polynomial) constraints (e.g., [39], =-=[19]-=-, [3]). Note that with linear constraints, each constraint represents a hyperplane ( ˆ ) or halfspace (>, ,<, ); a conjunction of constraints can represent a point, part of a hyperplane, or a convex p... |

16 | Gucht, On the Desirability and Limitations of Linear Spatial Database Models
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Citation Context ..., describing a single point. Various classes of constraints with different expressive power have been studied, for example, polynomial constraints [24], [29] or linear (polynomial) constraints (e.g., =-=[39]-=-, [19], [3]). Note that with linear constraints, each constraint represents a hyperplane ( ˆ ) or halfspace (>, ,<, ); a conjunction of constraints can represent a point, part of a hyperplane, or a co... |

14 | Voronoi diagrams of moving points in higher dimensional spaces - Albers, Roos - 1992 |

10 |
Modelling the Temporal Element in Land Information Systems
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(Show Context)
Citation Context ...described. Two papers that explicitly deal with spatio-temporal examples and models are [18], [7]. Several papers in the GIS literature study storage schemes for stepwise changing region values [22], =-=[30]-=-, [31], [5]. The general idea is to use a start version and then record the changes. Some work addresses spatio-temporal modeling within multimedia documents. In [40] the assumption is that objects ar... |

10 | An Introduction to Spatial Database Systems - Gting - 1994 |

9 | Second-Order Signature: A Tool for Specifying Data Models - Gting - 1993 |

8 |
An Efficient Hierarchical Data Structure for the U.S
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Citation Context ...wo papers that explicitly deal with spatio-temporal examples and models are [18], [7]. Several papers in the GIS literature study storage schemes for stepwise changing region values [22], [30], [31], =-=[5]-=-. The general idea is to use a start version and then record the changes. Some work addresses spatio-temporal modeling within multimedia documents. In [40] the assumption is that objects are rectangle... |

7 | Realm-Based Spatial Data Types - Gting, Schneider - 1995 |

6 | Modeling moving objects in multimedia database
- Nabil, AHH, et al.
- 1997
(Show Context)
Citation Context ...ationships are represented by a set of operators that apart from the relationship maintain its causality. This model does not cover motion and does not address arbitrary or changing object shapes. In =-=[26]-=- a model for moving objects in a multimedia scene is proposed. Objects are represented in terms of their trajectory, as discrete snapshots. A set of objects comprises a scene represented as a graph. E... |

5 |
Compact Voronoi diagrams for moving
- Guibas, Snoeyink, et al.
(Show Context)
Citation Context ...nt of relationships between objects. It also does not address changes in the shape of objects. Computational geometry has also shown interest in time-varying spatial objects. For instance, [1], [10], =-=[16]-=- deal with Voronoi diagrams of moving points. The task is to maintain the Voronoi diagram when a set of points is moving continuously over time. 5. Conclusions and future work We have proposed a new a... |

5 | A Foundation for Representing and Querying SpatioTemporal Data. Manuscript in preparation - Güting, Böhlen, et al. - 1998 |

4 |
An SQL-Like Seamless Query of Spatio-Temporal Data
- Gadia, Chopra, et al.
- 1993
(Show Context)
Citation Context ... of specialized spatial or temporal models to incorporate the other dimension. Most modeling approaches adopt the snapshot view, i.e., represent space-time data as a series of snapshots. Gadia et al. =-=[15]-=- propose time- and space-stamping of thematic attributes as a method to capture their timeand space-varying values. The time dimension describes when an attribute value is valid, and the spatial dimen... |

4 | Storing and Retrieving Changes in a Sequence of Polygons. Int - Kämpke - 1994 |

3 |
Voronoi diagrams of moving points in the plane, Int
- Fu, Lee
- 1991
(Show Context)
Citation Context ...olvement of relationships between objects. It also does not address changes in the shape of objects. Computational geometry has also shown interest in time-varying spatial objects. For instance, [1], =-=[10]-=-, [16] deal with Voronoi diagrams of moving points. The task is to maintain the Voronoi diagram when a set of points is moving continuously over time. 5. Conclusions and future work We have proposed a... |

3 | A foundation for representing and querying moving objects, Fern Universitt - Gting, Bhlen, et al. - 1998 |

3 | Temporal and SpatioTemporal Data Models and Their Expressive Power,” CHOROCHRONOS - Erwig, Scheider, et al. - 1997 |

2 |
Fundamentals of Algebraic Specications
- Ehrig, Mahr
- 1985
(Show Context)
Citation Context ...operators. So the carrier set for a type t contains the possible values for t, and the functions are mappings between the carrier sets. For a formal de®nition of many-sorted signature and algebra see =-=[9]-=- or [12]. Now it is important to understand that one can make such designs at two different levels of abstraction, namely as abstract or as discrete models. 3.3.1. Abstract models are simple. . . Abst... |

1 |
Second-Order Signature: A Tool for Specifying Data Models
- GuÈting
- 1993
(Show Context)
Citation Context ...rs. So the carrier set for a type t contains the possible values for t, and the functions are mappings between the carrier sets. For a formal de®nition of many-sorted signature and algebra see [9] or =-=[12]-=-. Now it is important to understand that one can make such designs at two different levels of abstraction, namely as abstract or as discrete models. 3.3.1. Abstract models are simple. . . Abstract mod... |

1 |
A Foundation for Representing and Querying Moving Objects. FernUniversitaÈt Hagen, Informatik-Report 238
- GuÈting, BoÈhlen, et al.
(Show Context)
Citation Context ...a structures and algorithms for the discrete model, and implementation. We recently completed the systematic design and formal de®nition of a system of data types and operations at the abstract level =-=[14]-=-. We plan to de®ne a part of this design as a discrete model. Our own choice is to use linear descriptions for the mpoint and mregion types as well as for the spatial types (line, region) but to use (... |

1 |
Implementation of the ROSE Algebra: Ef®cient Algorithms for Realm-Based Spatial Data Types
- Ridder, Schneider
- 1995
(Show Context)
Citation Context ...es on which they are based. As far as the design of data structures and algorithms and implementation are concerned, similar work has been done earlier for spatial databases in the ROSE algebra [20], =-=[17]-=-. Acknowledgments We are grateful to our partners in the CHOROCHRONOS project for asking many of the questions addressed in this paper. Thanks for many clarifying discussions especially to Mike BoÈhle... |

1 |
Storing and Retrieving Changes in a Sequence of Polygons,'' Int
- KaÈmpke
- 1994
(Show Context)
Citation Context ...an be described. Two papers that explicitly deal with spatio-temporal examples and models are [18], [7]. Several papers in the GIS literature study storage schemes for stepwise changing region values =-=[22]-=-, [30], [31], [5]. The general idea is to use a start version and then record the changes. Some work addresses spatio-temporal modeling within multimedia documents. In [40] the assumption is that obje... |

1 | Storing and Retrieving Changes in a Sequence of Polygons. Int - Kmpke - 1994 |

1 | A Foundation for Representing and Querying Spatio-Temporal Data. Manuscript in preparation - Gting, Bhlen, et al. - 1998 |