Classes of Spatiotemporal Objects and Their Closure Properties

A \emph{temporal graph} is, informally speaking, a graph that changes with time. When time is discrete and only the relationships between the participating entities may change and not the entities themselves, a temporal graph may be viewed as a sequence $G_1,G_2\ldots,G_l$ of static graphs over the same (static) set of nodes $V$. Though static graphs have been extensively studied, for their temporal generalization we are still far from having a concrete set of structural and ...

We explored ways of doing spatial search within a relational database: (1) hierarchical triangular mesh (a tessellation of the sphere), (2) a zoned bucketing system, and (3) representing areas as disjunctive-normal form constraints. Each of these approaches has merits. They all allow efficient point-in-region queries. A relational representation for regions allows Boolean operations among them and allows quick tests for point-in-region, regions-containing-point, and region-ov...

We describe our formal methods-based spatial reasoning framework BeSpaceD and its application in decision support for industrial automation. In particular we are supporting analysis and decisions based on formal models for industrial plant and mining operations. BeSpaceD is a framework for deciding geometric and topological properties of spatio-temporal models. We present an example and report on our ongoing experience with applications in different projects around software a...

We study geometric data structures for sets of point-based temporal events, answering time-windowed queries, i.e., given a contiguous time interval we answer common geometric queries about the point events with time stamps in this interval. The geometric queries we consider include queries based on the skyline, convex hull, and proximity relations of the point set. We provide space efficient data structures which answer queries in polylogarithmic time.

We study logic for reasoning with if-then formulas describing dependencies between attributes of objects which are observed in consecutive points in time. We introduce semantic entailment of the formulas, show its fixed-point characterization, investigate closure properties of model classes, present an axiomatization and prove its completeness, and investigate alternative axiomatizations and normalized proofs. We investigate decidability and complexity issues of the logic and...

Constructing complex queries on data which combines spatial, temporal, and spectral aspects is a challenging and error-prone process. Query interfaces of general-purpose database management systems fall short in providing intuitive support for users to effectively and efficiently construct queries. To address this situation, we developed GraphicalQueryBuilder, a tool which provides interactive and immediate feedback during query construction and visually represents search spa...

Cities are a big source of spatio-temporal data that is shared across entities to drive potential use cases. Many of the Spatio-temporal datasets are confidential and are selectively shared. To allow selective sharing, several access control models exist, however user cannot express arbitrary space and time constraints on data attributes using them. In this paper we focus on spatio-temporal access control model. We show that location and time attributes of data may decide its...

Given trajectories with gaps (i.e., missing data), we investigate algorithms to identify abnormal gaps in trajectories which occur when a given moving object did not report its location, but other moving objects in the same geographic region periodically did. The problem is important due to its societal applications, such as improving maritime safety and regulatory enforcement for global security concerns such as illegal fishing, illegal oil transfers, and trans-shipments. Th...

Consistent query answering is an inconsistency tolerant approach to obtaining semantically correct answers from a database that may be inconsistent with respect to its integrity constraints. In this work we formalize the notion of consistent query answer for spatial databases and spatial semantic integrity constraints. In order to do this, we first characterize conflicting spatial data, and next, we define admissible instances that restore consistency while staying close to t...

In this paper we present a semantic study of motion complexes (ie. of a motion verb followed by a spatial preposition). We focus on the spatial and the temporal intrinsic semantic properties of the motion verbs, on the one hand, and of the spatial prepositions, on the other hand. Then, we address the problem of combining these basic semantics in order to formally and automatically derive the spatiotemporal semantics of a motion complex from the spatiotemporal properties of it...