The management of moving objects has been intensively studied in the recent years. A wide and increasing range of database applications has to deal with spatial objects whose position changes continuously over time, called moving objects. Due to the continuous and unpredictable nature of the movements, they cannot be precisely stored in a database, and therefore objects’ positions are sampled, and between these sampled positions interpolation is used. This sampling/interpolation approach results in uncertainty in the objects’ positions in the whole trajectory of the moving objects. In this paper, we try to analyze this problem about uncertainty when the movement is restricted to a network. Examples of such movements are cars in highways and trains in railroads. The uncertainty problem is simpler in such cases compared to the free movement in 2-dimensional space. We describe the geometry of the uncertain trajectories of the objects with movement constrained to networks, an extension to the framework in [18, 16] to support uncertainty, as well as some implementation considerations using Secondo, an extensible database system that supports nonstandard applications.

Victor Teixeira de Almeida Ralf Hartmut Guting Praktische Informatik IV Fernuniversitat Hagen, D-58084 Hagen, Germany {victor.almeida, rhg}@fernuni-hagen.de Abstract studied in recent years. A wide and increasing range of database applications has to deal with spatial objects whose position changes continuously over time. The main interest of these applications is to e#ciently store and query the positions of these objects. To achieve this goal, index structures are required. Most of the proposals of index structures for moving objects deal with unconstrained 2-dimensional movement. The constrained movement is a special and a very important case of object movement. In this paper we propose a new index structure for moving objects in networks, the MON-Tree. We tested our proposal in an experimental evaluation with generated data sets. TheMON-Tree showed good scalability when increasing the number of objects and time units in the index structure, and the query window and time interval in querying.

We describe SECONDO, an extensible DBMS platform suitable for building research prototypes and for teaching architecture and implementation of database systems. It does not have a fixed data model, but is open for implementation of new models. SECONDO consists of three major components which can be used together or independently: (i) the kernel, which offers query processing over a set of implemented algebras, each offering some type constructors and operators, (ii) the optimizer, which implements the essential part of an SQL-like language, and (iii) the graphical user interface which is extensible by viewers for new data types and which provides a sophisticated viewer for spatial and spatio-temporal (moving) objects. Examples of algebras implemented in SECONDO are relations, spatial data types, R-trees, or midi objects (music files), each with suitable operations. The kernel is extensible by algebras, the optimizer by optimization rules and cost functions, and the GUI by viewers and display functions. A highlight of the description is a new algorithm for conjunctive query optimization which is remarkably simple, yet performs very well. We also emphasize a technique for selectivity estimation suitable for an extensible environment with complex algebras for non-standard data types.

Abstract. This paper concerns the efficient processing of multiple k nearest neighbor queries in a road-network setting. The assumed setting covers a range of scenarios such as the one where a large population of mobile service users that are constrained to a road network issue nearest-neighbor queries for points of interest that are accessible via the road network. Given multiple k nearest neighbor queries, the paper proposes progressive techniques that selectively cache query results in main memory and subsequently reuse these for query processing. The paper initially proposes techniques for the case where an upper bound on k is known a priori and then extends the techniques to the case where this is not so. Based on empirical studies with real-world data, the paper offers insight into the circumstances under which the different proposed techniques can be used with advantage for multiple k nearest neighbor query processing. 1

The constant increase of moving object data imposes the need for modeling, processing, and mining trajectories, in order to find and understand the patterns behind these data. Existing works have mainly focused on the geometric properties of trajectories, while the semantics and the background geographic information has rarely been addressed. We claim that meaningful patterns can only be extracted from trajectories if the geographic space where trajectories are located is considered. In this paper we propose a reverse engineering framework for mining and modeling semantic trajectory patterns. Since trajectory patterns are data dependent, they may not be modeled in conceptual geographic database schemas before they are known. Therefore, we apply data mining to extract general trajectory patterns, and through a new kind of relationships, we model these patterns in the geographic database schema. A case study shows the power of the framework for modeling semantic trajectory patterns in the geographic space.

This document presents a method to design scalable and representative moving object data (MOD) and a set 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. 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. 1

This work addresses the problem of obtaining the degree of similarity between trajectories of moving objects. Typically, a Moving Objects Database (MOD) contains sequences of (location,time) points describing the motion of individual objects, however, they also have an implicit information about the velocity, which is an important attribute describing the dynamics of a particular object. Our main goal is to extend the MOD functionalities with the capability of reasoning about how similar are the trajectories of objects that, possibly, move along geographically different routes. Towards this, we use a distance function which balances the lack of temporal-awareness of the Hausdorff distance with the generality (and complexity of calculation) of the Fréchet distance. Based on the observation that, as a firstapproximation in practice, the individual segments of trajectories are assumed to have constant speed, we provide efficient algorithms for: (1) optimal matching between trajectories; and (2) approximate matching between trajectories, both under translations and rotations, where the approximate algorithm guarantees a bounded error-quality with respect to the optimal one.

Because of the large amount of trajectory data produced by mobile devices, there is an increasing need for mechanisms to extract knowledge from this data. Most existing works have focused on the geometric properties of trajectories, but recently emerged the concept of semantic trajectories, in which the background geographic information is integrated to trajectory sample points. In this new concept, trajectories are observed as a set of stops and moves, where stops are the most important parts of the trajectory. Stops and moves have been computed by testing the intersections of trajectories with a set of geographic objects given by the user. In this paper we present an alternative solution with the capability of finding interesting places that are not expected by the user. The proposed solution is a spatiotemporal clustering method, based on speed, to work with single trajectories. We compare the two different approaches with experiments on real data and show that the computation of stops using the concept of speed can be interesting for several applications.

Many applications of spatio-temporal databases require support for sequenced spatio-temporal (SST) aggregation, e.g., when analyzing traffic density in a city. Conceptually, an SST aggregation produces one aggregate value for each point in time and space. This paper is the first to propose a method to efficiently evaluate SST aggregation queries for the COUNT, SUM, and AVG aggregation functions. Based on a discrete time model and a discrete, 1.5 dimensional space model that represents a road network, we generalize the concept of (temporal) constant intervals towards constant rectangles that represent maximal rectangles in the space-time domain over which the aggregation result is constant. We propose a new data structure, termed SST-tree, which extends the Balanced Tree for one-dimensional temporal aggregation towards the support for two-dimensional, spatio-temporal aggregation. The main feature of the Balanced Tree to store constant intervals in a compact way by using two counters is extended towards a compact representation of constant rectangles in the space-time domain. We propose and evaluate two variants of the SST-tree. The SST T-tree and SST H-tree use trees and hashmaps to manage spacestamps, respectively. Our experiments show that both solutions outperform a brute force approach in terms of memory and time. The SST H-tree is more efficient in terms of memory, whereas the SST T-tree is more efficient in terms of time. 1.

Abstract. Trajectory data play a fundamental role to an increasing number of applications, such as transportation management, urban planning and tourism. Trajectory data are normally available as sample points. However, for many applications, meaningful patterns cannot be extracted from sample points without considering the background geographic information. In this paper we propose a novel framework for semantic trajectory knowledge discovery. We propose to integrate trajectory sample points to the geographic information which is relevant to the application. Therefore, we extract the most important parts of trajectories, which are stops and moves, before applying data mining methods. Empirically we show the application and usability of our approach. 1.