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22
GraphDB: Modeling and Querying Graphs in Databases
 Proc. of the 20th VLDB Conference
, 1994
"... We propose a data model and query language that integrates an explicit modeling and querying of graphs smoothly into a standard database environment. For standard applications, some key features of objectoriented modeling are offered such as object classes organized into a hierarchy, object identit ..."
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Cited by 46 (2 self)
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We propose a data model and query language that integrates an explicit modeling and querying of graphs smoothly into a standard database environment. For standard applications, some key features of objectoriented modeling are offered such as object classes organized into a hierarchy, object identity, and attributes referencing objects. Querying can be done in a familiar style with a derive statement that can be used like a select... from... where. On the other hand, the model allows for an explicit representation of graphs by partitioning object classes into simple classes, link classes, and path classes whose objects can be viewed as nodes, edges, and explicitly stored paths of a graph (which is the whole database instance). For querying graphs, the derive statement has an extended meaning in that it allows one to refer to subgraphs of the database graph. A powerful rewrite operation is offered for the manipulation of heterogeneous sequences of objects which often occur as a result of accessing the database graph. Additionally there are special graph operations like determining a shortest path or a subgraph and the model is extensible by such operations. Besides being attractive for standard applications, the model permits a natural representation and sophisticated querying of networks, in particular of spatially embedded networks like highways, public transport, etc.
Vague regions
 5TH INT. SYMP. ON ADVANCES IN SPATIAL DATABASES, LNCS 1262
, 1997
"... In many geographical applications there is a need to model spatial phenomena not simply by sharp objects but rather through indeterminate or vague concepts. To support such applications we present a model of vague regions which covers and extends previous approaches. The formal framework is based on ..."
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Cited by 41 (20 self)
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In many geographical applications there is a need to model spatial phenomena not simply by sharp objects but rather through indeterminate or vague concepts. To support such applications we present a model of vague regions which covers and extends previous approaches. The formal framework is based on a general exact model of spatial data types. On the one hand, this simplifies the definition of the vague model since we can build upon already existing theory of spatial data types. On the other hand, this approach facilitates the migration from exact to vague models. Moreover, exact spatial data types are subsumed as a special case of the presented vague concepts. We present examples and show how they are represented within our framework. We give a formal definition of basic operations and predicates which particularly allow a more finegrained investigation of spatial situations than in the pure exact case. We also demonstrate the integration of the presented concepts into an SQLlike query language.
Modeling and Querying Moving Objects in Networks
 VLDB J
, 2004
"... 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. ..."
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Cited by 34 (7 self)
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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.
Developments in SpatioTemporal Query Languages
, 1999
"... Integrating spatiotemporal data as abstract data types into already existing data models is a promising approach to creating spatiotemporal query languages. In this context, an important new class of queries can be identified which is concerned with developments of spatial objects over time, that ..."
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Cited by 31 (12 self)
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Integrating spatiotemporal data as abstract data types into already existing data models is a promising approach to creating spatiotemporal query languages. In this context, an important new class of queries can be identified which is concerned with developments of spatial objects over time, that is, queries ask especially for changes in spatial relationships. Based on a definition of the notion of spatiotemporal predicate we provide a framework which allows to build more and more complex predicates starting with a small set of elementary ones. These predicates can be well used to characterize developments. We show how these concepts can be realized within the relational data model. In particular, we demonstrate how SQL can be extended to enable the querying of developments.
SecondOrder Signature: A Tool for Specifying Data Models
 Query Processing, and Optimization. Proc. ACM SIGMOD Conf
, 1993
"... We propose a framework for the specification of extensible database systems. A particular goal is to implement a software component for parsing and rulebased optimization that can be used with widely varying data models and query languages as well as representation and query processing systems. T ..."
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Cited by 29 (19 self)
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We propose a framework for the specification of extensible database systems. A particular goal is to implement a software component for parsing and rulebased optimization that can be used with widely varying data models and query languages as well as representation and query processing systems. The key idea is to use secondorder signature (and algebra), a system of two coupled manysorted signatures, where the toplevel signature offers kinds and type constructors and the bottomlevel signature provides polymorphic operations over the types defined as terms of the top level. Hence the top level can be used to define a data or representation model and the bottom level to describe a query algebra or a query processing algebra. We show the applicability of this framework by examples drawn from relational modeling and query processing.
Partition and conquer
 In 3rd Int. Conf. on Spatial Information Theory, LNCS 1329
, 1997
"... Abstract. Although maps and partitions are ubiquitous in geographical information systems and spatial databases, there is only little work investigating their foundations. We give a rigorous definition for spatial partitions and propose partitions as a generic spatial data type that can be used to m ..."
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Cited by 21 (7 self)
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Abstract. Although maps and partitions are ubiquitous in geographical information systems and spatial databases, there is only little work investigating their foundations. We give a rigorous definition for spatial partitions and propose partitions as a generic spatial data type that can be used to model arbitrary maps and to support spatial analysis. We identify a set of three powerful operations on partitions and show that the type of partitions is closed under them. These basic operators are sufficient to express all known applicationspecific operations. Moreover, many map operations will be considerably generalized in our framework. We also indicate that partitions can be effectively used as a metamodel to describe other spatial data types. 1
Spatiotemporal Network Databases and Routing Algorithms: A Summary of Results
 Proceedings of International Symposium on Spatial and Temporal Databases (SSTD’07
, 2007
"... Transportation. The content of this work does not necessarily reflect the position or policy of the government and no official ..."
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Cited by 19 (9 self)
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Transportation. The content of this work does not necessarily reflect the position or policy of the government and no official
Generalizing Graphs using Amalgamation and Selection
 Advances in Spatial Databases. 6th International Symposium, SSD'99, volume 1651 of Lecture Notes in Computer Science
, 1999
"... . This work is a contribution to the developing literature on multiresolution data models. It considers operations for modeloriented generalization in the case where the underlying data is structured as a graph. The paper presents a new approach in that a distinction is made between generalization ..."
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Cited by 18 (5 self)
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. This work is a contribution to the developing literature on multiresolution data models. It considers operations for modeloriented generalization in the case where the underlying data is structured as a graph. The paper presents a new approach in that a distinction is made between generalizations that amalgamate data objects and those that select data objects. We show that these two types of generalization are conceptually distinct, and provide a formal framework in which both can be understood. Generalizations that are combinations of amalgamation and selection are termed simplifications, and the paper provides a formal framework in which simplifications can be computed (for example, as compositions of other simplifications). A detailed case study is presented to illustrate the techniques developed, and directions for further work are discussed. 1 Introduction Specialist spatial information systems (SIS) play an increasingly important role within the Information Tech...
The Graph Voronoi Diagram with Applications
 Networks
, 2000
"... The Voronoi diagram is a famous structure of computational geometry. We show that there is a straightforward equivalent in graph theory which can be efficiently computed. In particular, we give two algorithms for the computation of graph Voronoi diagrams, prove a lower bound on the problem, and we i ..."
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Cited by 14 (0 self)
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The Voronoi diagram is a famous structure of computational geometry. We show that there is a straightforward equivalent in graph theory which can be efficiently computed. In particular, we give two algorithms for the computation of graph Voronoi diagrams, prove a lower bound on the problem, and we identify cases where the algorithms presented are optimal. The space requirement of a graph Voronoi diagram is modest, since it needs no more space than the graph itself. The investigation of graph Voronoi diagrams is motivated by many applications and problems on networks that can be easily solved with their help. This includes the computation of nearest facilities, all nearest neighbors and closest pairs, some kind of collision free moving, and anticenters and closest points. 1 Introduction The Voronoi diagram is a data structure extensively investigated in the domain of computational geometry [14]. Originally, it characterizes regions of proximity for a set of k sites in the pl...
Granulation for Graphs
 Spatial Information Theory. Cognitive and Computational Foundations of Geographic Information Science. International Conference COSIT'99, volume 1661 of Lecture Notes in Computer Science
, 1999
"... . In multiresolution data handling, a less detailed structure is often derived from a more detailed one by amalgamating elements which are indistinguishable at the lower level of detail. This gathering together of indistinguishable elements is called a granulation of the more detailed structure ..."
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Cited by 10 (6 self)
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. In multiresolution data handling, a less detailed structure is often derived from a more detailed one by amalgamating elements which are indistinguishable at the lower level of detail. This gathering together of indistinguishable elements is called a granulation of the more detailed structure. When handling spatial data at several levels of detail the granulation of graphs is an important topic. The importance of graphs arises from their widespread use in modelling networks, and also from the use of dual graphs of spatial partitions. This paper demonstrates that there are several quite different kinds of granulation for graphs. Four kinds are described in detail, and situations where some of these may arise in spatial information systems are indicated. One particular kind of granulation leads to a new formulation of the boundarysensitive approach to qualitative location developed by Bittner and Stell. Vague graphs and their connection with granulation are also discusse...