Thomas Behr

Topological relationships between complex spatial objects

For a long time topological relationships between spatial objects have been a focus of research in a number of disciplines like artificial intelligence, cognitive science, linguistics, robotics, and spatial reasoning. Especially as predicates they support the design of suitable query languages for spatial data retrieval and analysis in spatial databases and geographical information systems (GIS). Unfortunately, they have so far only been defined for and applicable to simplified abstractions of spatial objects like single points, continuous lines, and simple regions. With the introduction of complex spatial data types an issue arises regarding the design, definition, and number of topological relationships operating on these complex types. This article closes this gap and first introduces definitions of general and versatile spatial data types for complex points, complex lines, and complex regions. Based on the well known 9-intersection model, it then determines the complete sets of mutually exclusive topological relationships for all type combinations. Completeness and mutual exclusion are shown by a proof technique called proof-by-constraint-and-drawing. Due to the resulting large numbers of predicates and the difficulty of handling them, the user is provided with the concepts of topological cluster predicates and topological predicate groups, which permit one to reduce the number of predicates to be dealt with in a user-defined and/or application-specific manner.

BerlinMOD: a benchmark for moving object databases

This document presents a method to design scalable and representative moving object data (MOD) and two sets of queries for benchmarking spatio-temporal DBMS. Instead of programming a dedicated generator software, we use the existing Secondo DBMS to create benchmark data. The benchmark is based on a simulation scenario, where the positions of a sample of vehicles are observed for an arbitrary period of time within the street network of Berlin. We demonstrate the data generator’s extensibility by showing how to achieve more natural movement generation patterns, and how to disturb the vehicles’ positions to create noisy data. As an application and for reference, we also present first benchmarking results for the Secondo DBMS. Whereas the benchmark focuses on range queries, we demonstrate its ability to incorporate new future classes of queries by presenting a preliminary extension handling various nearest neighbour queries. Such a benchmark is useful in several ways: It provides well-defined data sets and queries for experimental evaluations; it simplifies experimental repeatability; it emphasizes the development of complete systems; it points out weaknesses in existing systems motivating further research. Moreover, the BerlinMOD benchmark allows one to compare different representations of the same moving objects.

Efficient k-nearest neighbor search on moving object trajectories

With the growing number of mobile applications, data analysis on large sets of historical moving objects trajectories becomes increasingly important. Nearest neighbor search is a fundamental problem in spatial and spatio-temporal databases. In this paper, we consider the following problem: Given a set of moving object trajectories D and a query trajectory mq, find the k nearest neighbors to mq within D for any instant of time within the lifetime of mq. We assume D is indexed in a 3D-R-tree and employ a filter-and-refine strategy. The filter step traverses the index and creates a stream of so-called units (linear pieces of a trajectory) as a superset of the units required to build the result of the query. The refinement step processes an ordered stream of units and determines the pieces of units forming the precise result. To support the filter step, for each node p of the index, in preprocessing a time-dependent coverage function Cp(t) is computed which is the number of trajectories represented in p present at time t. Within the filter step, sophisticated data structures are used to keep track of the aggregated coverages of the nodes seen so far in the index traversal to enable pruning. Moreover, the R-tree index is built in a special way to obtain coverage functions that are effective for pruning. As a result, one obtains a highly efficient kNN algorithm for moving data and query points that outperforms the two competing algorithms by a wide margin. Implementations of the new algorithms and of the competing techniques are made available as well. Algorithms can be used in a system context including, for example, visualization and animation of results. Experiments of the paper can be easily checked or repeated, and new experiments be performed.

Querying Moving Objects in SECONDO

Representing descriptions of movements in databases and querying them is a basic capability required in mobile data management. In this demonstration, we show for the first time a prototype implementing a data model and query language for moving objects (trajectories) completely integrated into a DBMS environment, including query optimization and user interface issues such as animation.

Topological Relationships of Complex Points and Complex Regions

Topological relationships between spatial objects have been a focus of research on spatial data handling and reasoning for a long time. Especially as predicates they support the design of suitable query languages for spatial data retrieval and analysis in databases. Unfortunately, they are so far only applicable to simplified abstractions of spatial objects like single points, continuous lines, and simple regions, as they occur in systems like current geographical information systems and spatial database systems. Since these abstractions are usually not sufficient to cope with the complexity of geographic reality, their generalization is needed which especially has influence on the nature, definition, and number of their topological relationships. This paper partially closes this gap and first introduces very general spatial data types for complex points and complex regions. It then defines the corresponding complete sets of mutually exclusive, topological relationships.

Exploring spatiotemporal patterns by integrating visual analytics with a moving objects database system

In previous work, we have proposed a tool for Spatiotemporal Pattern Query. It matches individual moving object trajectories against a given movement pattern. For example, it can be used to find the situations of Missed Approach in ATC data (Air Traffic Control systems, used for tracking the movement of aircrafts), where the landing of the aircraft was interrupted for some reason. This tool expresses the pattern as a set of predicates that must be fulfilled in a certain temporal order. It is implemented as a Plugin to the Secondo DBMS system. Although the tool is generic and flexible, domain expertise is required to formulate and tune queries. The user has to decide the set of predicates, their arguments, and the temporal constraints that best describe the pattern. This paper demonstrates a novel solution where a Visual Analytics system, V-Analytics, is used in integration with this query tool to help a human analyst explore such patterns. The demonstration is based on a real ATC data set.

Fuzzy spatial objects: an algebra implementation in SECONDO

This paper describes a data model for fuzzy spatial objects implemented as an algebra module in SECONDO. Furthermore, the graphical representation of such objects is discussed.

Representation of periodic moving objects in databases

In the real world, lots of objects with changing position can be found. Some of them repeat the same movement several times, called periodic movements. Examples include airplanes, trains, planets, and marine turtles. This paper describes a model for representing the periodic movements to be stored in a database system, exploiting the information about the repetitions. The model is generic enough to represent any kind of movement, not being restricted to objects with repetitions in their movement. We present algorithms to detect the repetitions and to convert to the periodic representation as well as the implementation of some operations on such representation. We show, in an experimental evaluation against the so-called flat representation, that the approach presented in this paper significantly improves the performance of query processing in a database system when dealing with objects with some periodic movement. We also show that, for the worst case where the objects do not follow any periodic movement at all, our approach still performs acceptably.

Nearest Neighbor Search on Moving Object Trajectories in Secondo

In the context of databases storing histories of movement (also called trajectories), we present two query processing operators to compute the k nearest neighbors of a moving query point within a set of moving points. Data moving points are represented as collections of point units (i.e., a time interval together with a linear movement function). The first operator, knearest , processes a stream of units arriving ordered by start time and returns the set of units representing the k nearest neighbors over time. It can be used to process a set of moving point candidates selected by other conditions. The second operator, knearestfilter , operates on a set of units indexed in an R-tree and uses some novel pruning techniques. It returns a set of candidates that can be further processed by knearest to obtain the final answer. These nearest neighbor algorithms are presented within Secondo , a complete DBMS environment for handling moving object histories. For example, candidates and final results can be visualized and animated at the user interface.