Algebras for Moving Objects and Their Implementation.
Ralf Hartmut Güting · 2004
The general goal of the work described in the sequel is to provide support for time-dependent geometries, or moving objects, in databases. Hence we would like to find extensions to DBMS data models and query languages that allows us to model moving objects and to formulate all kinds of queries about such movements. This needs to be supported by corresponding extensions of the DBMS implementation such as new data structures and algorithms, indexes, optimization rules, cost functions, etc. Systems of spatial data types and operations, or spatial algebras, are a key concept in the modeling and implementation of spatial database systems. The idea can be extended to spatio-temporal databases by introducing spatio-temporal types. A basic assumption is that geometries can change continuously (whereas the earlier work generally supported only discrete changes). To emphasize the capability of continuous change, we speak of moving objects. Hence we have data types such as moving point, describing an entity for which only the time-dependent position in space is of relevance, or moving region, a time-dependent area for which also the extent is relevant, hence, which can not only move, but also grow or shrink. A value of type moving point might represent, for example, the trip of a person or vehicle (embedded in space and time); a value of type moving region might represent the growth of a forest, a forest fire, or an oil spill in the sea. In the sequel we first briefly illustrate this approach. At a conceptual, or abstract level, a value of type moving point (type mpoint, for short) is a function from time into point values, and a moving region (mregion) value is a function from time into region values. Such values exist in a three-dimensional (2D + time) space, as illustrated in Figure 1. Data types may be embedded in the role of attribute types into a DBMS data model. For example, in a relational setting, we may have relations to represent the movements of air planes or storms: