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Explicit Graphs in a Functional Model for Spatial Databases
October 1994 (vol. 6 no. 5)
pp. 787-804

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 hierarchies, graphs are available as an explicit modeling tool, and graph operations are part of the query language. 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. Furthermore, 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 capabilities for spatial databases, in particular for spatially embedded networks such as highways, rivers, public transport, and so forth. We use multilevel 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 constructors as functions between kinds, and so provides the types that can be used at the first level.

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Index Terms:
visual databases; database theory; graph theory; query languages; query processing; spatial databases; explicit graphs; functional model; data model; query language; graph structures; data modeling; order-sorted algebra; data type hierarchies; object hierarchies; explicit modeling tool; nodes; edges; explicit paths; object type hierarchy; dynamic generalization; spatial data types; spatially embedded networks; public transport; rivers; highways; multilevel order-sorted algebra
Citation:
M. Erwig, R.H. Güting, "Explicit Graphs in a Functional Model for Spatial Databases," IEEE Transactions on Knowledge and Data Engineering, vol. 6, no. 5, pp. 787-804, Oct. 1994, doi:10.1109/69.317707
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