Spatio-temporal databases deal with geometries changing over time. The goal of our work is to provide a DBMS data model and query language capable of handling such time-dependent geometries, including those changing continuously which describe moving objects. Two fundamental abstractions are moving point and moving region, describing objects for which only the time-dependent position, or position and extent, are of interest, respectively. We propose to represent such time-dependent geometries as attribute data types with suitable operations, that is, to provide an abstract data type extension to a DBMS data model and query language. This paper presents a design of such a system of abstract data types. It turns out that besides the main types of interest, moving point and moving region, a relatively large number of auxiliary data types is needed. For example, one needs a line type to represent the projection of a moving point into the plane, or a "moving real" to represent the time-dependent distance of two moving points. It then becomes crucial to achieve (i) orthogonality in the design of the type system, i.e., type constructors can be applied uniformly, (ii) genericity and consistency of operations, i.e., operations range over as many types as possible and behave consistently, and (iii) closure and consistency between structure and operations of non-temporal and related temporal types. Satisfying these goals leads to a simple and expressive system of abstract data types that may be integrated into a query language to yield apowerful language for querying spatio-temporal data, including moving objects. The paper formally defines the types and operations, offers detailed insight into the considerations that went into the design, and exempli es the use of the abstract data types using SQL. The paper o ers a precise and conceptually clean foundation for implementing a spatio-temporal DBMS extension.

Spatial data types or algebras for database systems should (1) be fully general, that is, closed under set operations, (2) have formally defined semantics, (3) be defined in terms of finite representations available in computers, (4) offer facilities to enforce geometric consistency of related spatial objects, and (5) be in-dependent of a particular DBMS data model, but cooperate with any. We present an algebra that uses realms as geometric domains underlying spatial data types. A realm, as a general database concept, is a finite, dynamic, user-defined structure underlying one or more system data types. Problems of numerical robustness and topological correctness are solved within and below the realm layer so that spatial algebras defined above a realm have very nice algebraic properties. Realms also interact with a DMBS to enforce geometric consistency on object creation or up-date. The ROSE algebra is defined on top of realms and offers general types to represent point, line, and region features, together with a comprehensive set of operations. It is described within a polymorphic type system and interacts with a DMBS data model and query language through an abstract object model interface. An example integration of ROSE into the object-oriented data model 02 and its query language is presented.

Abstract: The ROSE algebra, defined earlier, is a system of spatial data types for use in spatial database systems. It offers data types to represent points, lines, and regions in the plane together with a comprehensive set of operations; semantics of types and operations have been formally defined. Values of these data types have a quite general structure, e.g. an object of type regions may consist of several polygons with holes. All ROSE objects are realm-based which means all points and vertices of objects lie on an integer grid and no two distinct line segments of any two objects intersect in their interior. In this paper we describe the implementation of the ROSE algebra, providing data structures for the types and new realm-based geometric algorithms for the operations. The main techniques used are (parallel) traversal of objects, plane-sweep, and graph algorithms. All algorithms are analyzed with respect to their worst case time and space requirements. Due to the realm properties, these algorithms are relatively simple, efficient, and numerically completely robust. All data structures and algorithms have indeed been implemented in the ROSE system; the Modula-2 source code is freely available from the authors for study or use.

Whereas earlier work on spatio-temporal databases generally focused on geometries changing in discrete steps, the emerging area of moving objects databases supports geometries changing continuously. Two important abstractions are moving point and moving region, modeling objects for which only the time-dependent position, or also the shape and extent are relevant, respectively. Examples of the first kind of moving entity are all kinds of vehicles, aircraft, people, or animals; of the latter hurricanes, forest res, forest growth, or oil spills in the sea. The goal is to develop data models and query languages as well as DBMS implementations supporting such entities, enabling new kinds of database applications. In earlier work we have proposed an approach based on abstract data types. Hence, moving point or moving region are viewed as data types with suitable operations. For example, a moving point might be projected into the plane, yielding a curve, or a moving region be mapped to a function describing the development of its size, yielding a real-valued function. A careful design of a system of types and operations (an algebra) has been presented, emphasizing completeness, closure, consistency and genericity. This design was given at an abstract level, defining, for example, geometries in terms of infinite point sets. In the next step, a discrete model was presented, o ering nite representations and data structures for all the types of the abstract model. The present paper provides the final step towards implementation by studying and developing systematically algorithms for (a large subset of) the operations. Some of them are relatively straightforward; others are quite complex. Algorithms are meant to be used in a database context; we also address...

Moving Objects Databases have become an important research issue in recent years. For modeling and querying moving objects, there exists a comprehensive framework of abstract data types to describe objects moving freely in the 2D plane, providing data types such as moving point or moving region. However, in many applications people or vehicles move along transportation networks.

Observing that networks are ubiquitous in applications for spatial databases, we define a new data model and query language that especially supports graph structures. This model integrates concepts of functional data modeling with order-sorted algebra. Besides object and data type hierar-chies graphs are available as an explicit modeling tool, and graph operations are part of the query lan-guage. Graphs have three classes of components, namely nodes, edges, and explicit paths. These are at the same time object types within the object type hierarchy and can be used like any other type. Explicit paths are useful because “real world ” objects often correspond to paths in a network. Further-more, a dynamic generalization concept is introduced to handle heterogeneous collections of objects in a query. In connection with spatial data types this leads to powerful modeling and querying capa-bilities for spatial databases, in particular for spatially embedded networks such as highways, rivers, public transport, and so forth. We use multi-level order-sorted algebra as a formal framework for the specification of our model. Roughly spoken, the first level algebra defines types and operations of the query language whereas the second level algebra defines kinds (collections of types) and type con-structors as functions between kinds and so provides the types that can be used at the first level.

databases (MOD) is the modeling of moving objects. In this paper, a new moving objects database model, Moving Objects on Dynamic Transportation Networks (MODTN), is proposed. In MODTN, moving objects are modeled as moving graph points which move only within predefined transportation networks. To express general events of the system, such as traffic jams, temporary constructions, insertion and deletion of junctions or routes, the underlying transportation networks are modeled as dynamic graphs so that the state and the topology of the graph system at any time instant can be tracked and queried. Besides, to track the location of network constrained moving objects, a location update mechanism is provided, and the corresponding uncertainty management issues are analyzed.

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The management of moving objects has been intensively studied in the recent years. A wide and increasing range of database applications has to deal with spatial objects whose position changes continuously over time, called moving objects. Due to the continuous and unpredictable nature of the movements, they cannot be precisely stored in a database, and therefore objects’ positions are sampled, and between these sampled positions interpolation is used. This sampling/interpolation approach results in uncertainty in the objects’ positions in the whole trajectory of the moving objects. In this paper, we try to analyze this problem about uncertainty when the movement is restricted to a network. Examples of such movements are cars in highways and trains in railroads. The uncertainty problem is simpler in such cases compared to the free movement in 2-dimensional space. We describe the geometry of the uncertain trajectories of the objects with movement constrained to networks, an extension to the framework in [18, 16] to support uncertainty, as well as some implementation considerations using Secondo, an extensible database system that supports nonstandard applications.

In this paper, a State-Based Dynamic Transportation Network (SBDTN) model is presented, which can be used to describe the spatiotemporal aspect of temporally variable transportation networks. The basic idea of this model is to associate a temporal attribute to every node or edge of the graph system so that state changes (such as traffic jams and blockages caused by temporary constructions) and topology changes (such as insertion and deletion of nodes or edges) can be expressed. Since the changes of the graph system are discrete, the temporal attribute can be expressed as a series of temporal units and each temporal unit describes one single state of the node or edge during a certain period of time. The data model is given as a collection of data types and operations which can be plugged as attribute types into a DBMS to obtain a complete data model and query language.