A Theory of Spatio-temporal Database Queries

Abstract

Abstract. We address a fundamental question concerning spatio-temporal database systems: "What are exactly spatio-temporal queries?" We define spatio-temporal queries to be computable mappings that are also generic, meaning that the result of a query may only depend to a limited extent on the actual internal representation of the spatio-temporal data. Genericity is defined as invariance under transformations that preserve certain characteristics of spatio-temporal data (e.g., collinearity, distance, velocity, acceleration, ...) that are relevant to a database user. These transformations also respect the monotone nature of time. We investigate different genericity classes relative to the constraint database model for spatio-temporal databases and we identify sound and complete languages for the first-order, respectively the computable, queries in these genericity classes.

Affine-Invariant Triangulation of Spatio-Temporal Data with an Application to Image Retrieval

“…In the area of spatial database research, much attention has been payed to affine invariance of both data description and manipulation techniques and queries [12][13][14]. The main idea of working in an affine invariant way is to obtain methods and techniques that are not affected by affine transformations of the ambient space in which the data is situated.…”

“…Also, in computer graphics, affine-invariant norms and triangulations have been studied [19]. In the field of spatial and spatio-temporal constraint databases [20,21], affine-invariant query languages [12][13][14] have been proposed. For spatial data, there exist several triangulation algorithms, but, apart from the triangulation of Nielson [19], their output is not affine-invariant.…”

Trajectory Databases: Data Models, Uncertainty and Complete Query Languages

“…The proofs of these sound and completeness results are inspired by earlier work on complete languages for spatial [10] and spatio-temporal databases [4]. Compared to [4], the language we propose is far more user oriented since it is not based on geometric but speed-related predicates.…”

“…The proofs of these sound and completeness results are inspired by earlier work on complete languages for spatial [10] and spatio-temporal databases [4]. Compared to [4], the language we propose is far more user oriented since it is not based on geometric but speed-related predicates. We remark that the completeness and soundness results presented in this paper hold for arbitrary spatio-temporal data, but we present them for trajectory (sample) data for which the bead model is specifically designed.…”

“…We characterize this group V of transformations as the combinations of affinities of time with orthogonal transformations of space composed with a spatial scalings (that uses the same scale factor as the temporal affinity) and translations. In [4], transformations that leave the velocity vector invariant were discussed, but starting from spatial transformation that are a function of time alone. Our result holds in general, for arbitrary smooth transformations of time-space space.…”