(ii) a component-based design in which spatial, temporal and historical extensions are formalised incrementally, for subsequent use together or separately; (iii) compatibility with mainstream query processing frameworks for object databases; and (iv) the integration of the spatio-temporal proposal with the ODMG standard. Spatio-temporal extensions to data models have been an active area of research for a number of years. To date, much of this work has focused on the relational data model, with object data models receiving far less consideration. Where descriptions of such object models do exist, there is currently a lack of systems which build upon these models to 1

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This paper contributes a general approach to characterizing patterns of change in a spatio-temporal database. While there is a particular interest in modelling and querying how spatio-temporal entities evolve, the approach contributed by the paper is distinctive in being applicable without modification to aspatial entities as well. The paper uses the Tripod spatio-temporal model to describe and instantiate in detail the contributed approach. After briefly describing a typical application and providing basic knowledge about Tripod, the paper characterizes and classifies evolution queries and describes in detail how they are evaluated.

Abstract Spatio-temporal extensions to data models have been an active area of research for a number of years. To date, much of this work has focused on the relational data model, with object data models receiving far less consideration. This paper presents a spatio-historical object model that uses a specialized mechanism, called a history, to maintain knowledge about entities that change over time. Key features of the resulting proposal include: (i) consistent representations of primitive spatial and temporal types; (ii) a component-based design in which spatial, temporal and historical extensions are formalized incrementally, for subsequent use together or separately; (iii) a formally specified data model. The model can be used directly during the design of spatio-historical applications, but also forms the basis of an implementation activity developing a spatio-historical object database management system. 1

Spatio-temporal databases are often associated with analyses that summarize stored data over spatial, temporal or spatio-temporal dimensions. For example, a study of traffic patterns might explore average traffic densities on a road network at different times, over different areas in space, and over different areas in space at different times. The importance of temporal, spatial and spatio-temporal aggregation has been reflected in a significant number of proposals for algorithms for efficient computation of specific kinds of aggregation. However, although such proposals may be effective in particular cases, as yet there is no generic framework that provides efficient support for the wide range of partitioning and aggregation operations that a spatio-temporal database management system might be expected to support over both stored and derived data. This paper proposes an algorithmic framework that can be applied to many different forms of aggregation, and presents the results of performance studies on an implementation of the framework. These show that the framework provides a scalable solution for the many cases in which the aggregations required over stored and derived data may be widely variable and unpredictable.