Christian S. Jensen

Indexing the positions of continuously moving objects

The coming years will witness dramatic advances in wireless communications as well as positioning technologies. As a result, tracking the changing positions of objects capable of continuous movement is becoming increasingly feasible and necessary. The present paper proposes a novel, R*-tree based indexing technique that supports the efficient querying of the current and projected future positions of such moving objects. The technique is capable of indexing objects moving in one-, two-, and three-dimensional space. Update algorithms enable the index to accommodate a dynamic data set, where objects may appear and disappear, and where changes occur in the anticipated positions of existing objects. A comprehensive performance study is reported.

A foundation for representing and querying moving objects

Spatio-temporal databases deal with geometries changing over time. The goal of our work is to provide a DBMS data model and query language capable of handling such time-dependent geometries, including those changing continuously that describe moving objects. Two fundamental abstractions are moving point and moving region, describing objects for which only the time-dependent position, or position and extent, respectively, are of interest. We propose to present such time-dependent geometries as attribute data types with suitable operations, that is, to provide an abstract data type extension to a DBMS data model and query language. This paper presents a design of such a system of abstract data types. It turns out that besides the main types of interest, moving point and moving region, a relatively large number of auxiliary data types are needed. For example, one needs a line type to represent the projection of a moving point into the plane, or a “moving real” to represent the time-dependent distance of two points. It then becomes crucial to achieve (i) orthogonality in the design of the system, i.e., type constructors can be applied unifomly; (ii) genericity and consistency of operations, i.e., operations range over as many types as possible and behave consistently; and (iii) closure and consistency between structure and operations of nontemporal and related temporal types. Satisfying these goal leads to a simple and expressive system of abstract data types that may be integrated into a query language to yield a powerful language for querying spatio-temporal data, including moving objects. The paper formally defines the types and operations, offers detailed insight into the considerations that went into the design, and exemplifies the use of the abstract data types using SQL. The paper offers a precise and conceptually clean foundation for implementing a spatio-temporal DBMS extension.

Capturing the Uncertainty of Moving-Object Representations

Spatiotemporal applications, such as fleet management and air traffic control, involving continuously moving objects are increasingly at the focus of research efforts. The representation of the continuously changing positions of the objects is fundamentally important in these applications. This paper reports on on-going research in the representation of the positions of moving-point objects. More specifically, object positions are sampled using the Global Positioning System, and interpolation is applied to determine positions in-between the samples. Special attention is given in the representation to the quantification of the position uncertainty introduced by the sampling technique and the interpolation. In addition, the paper considers the use for query processing of the proposed representation in conjunction with indexing. It is demonstrated how queries involving uncertainty may be answered using the standard filter-and-refine approach known from spatial query processing.

Efficient retrieval of the top-k most relevant spatial web objects

The conventional Internet is acquiring a geo-spatial dimension. Web documents are being geo-tagged, and geo-referenced objects such as points of interest are being associated with descriptive text documents. The resulting fusion of geo-location and documents enables a new kind of top-k query that takes into account both location proximity and text relevancy. To our knowledge, only naive techniques exist that are capable of computing a general web information retrieval query while also taking location into account. This paper proposes a new indexing framework for location-aware top-k text retrieval. The framework leverages the inverted file for text retrieval and the R-tree for spatial proximity querying. Several indexing approaches are explored within the framework. The framework encompasses algorithms that utilize the proposed indexes for computing the top-k query, thus taking into account both text relevancy and location proximity to prune the search space. Results of empirical studies with an implementation of the framework demonstrate that the papers proposal offers scalability and is capable of excellent performance.

Discovery of convoys in trajectory databases

As mobile devices with positioning capabilities continue to proliferate, data management for so-called trajectory databases that capture the historical movements of populations of moving objects becomes important. This paper considers the querying of such databases for convoys, a convoy being a group of objects that have traveled together for some time. More specifically, this paper formalizes the concept of a convoy query using density-based notions, in order to capture groups of arbitrary extents and shapes. Convoy discovery is relevant for real-life applications in throughput planning of trucks and carpooling of vehicles. Although there has been extensive research on trajectories in the literature, none of this can be applied to retrieve correctly exact convoy result sets. Motivated by this, we develop three efficient algorithms for convoy discovery that adopt the well-known filter-refinement framework. In the filter step, we apply line-simplification techniques on the trajectories and establish distance bounds between the simplified trajectories. This permits efficient convoy discovery over the simplified trajectories without missing any actual convoys. In the refinement step, the candidate convoys are further processed to obtain the actual convoys. Our comprehensive empirical study offers insight into the properties of the papers proposals and demonstrates that the proposals are effective and efficient on real-world trajectory data.

Query and update efficient B + -tree based indexing of moving objects

A number of emerging applications of data management technology involve the monitoring and querying of large quantities of continuous variables, e.g., the positions of mobile service users, termed moving objects. In such applications, large quantities of state samples obtained via sensors are streamed to a database. Indexes for moving objects must support queries efficiently, but must also support frequent updates. Indexes based on minimum bounding regions (MBRs) such as the R-tree exhibit high concurrency overheads during node splitting, and each individual update is known to be quite costly. This motivates the design of a solution that enables the B+ -tree to manage moving objects. We represent moving-object locations as vectors that are timestamped based on their update time. By applying a novel linearization technique to these values, it is possible to index the resulting values using a single B+-tree that partitions values according to their timestamp and otherwise preserves spatial proximity. We develop algorithms for range and k nearest neighbor queries, as well as continuous queries. The proposal can be grafted into existing database systems cost effectively. An extensive experimental study explores the performance characteristics of the proposal and also shows that it is capable of substantially outperforming the R-tree based TPR-tree for both single and concurrent access scenarios.

Enabling Italian e-government through a cooperative architecture

Multidimensional database technology is a key factor in the interactive analysis of large amounts of data for decision making purposes. In contrast to previous technologies, these databases view data as multidimensional cubes that are particularly well suited for data analysis. Multidimensional models categorize data either as facts with associated numerical measures or as textual dimensions that characterize the facts. Queries aggregate measure values over a range of dimension values to provide results such as total sales per month of a given product. Multidimensional database technology is being applied to distributed data and to new types of data that current technology often cannot adequately analyze. For example, classic techniques such as preaggregation cannot ensure fast query response times when data-such as that obtained from sensors or GPS-equipped moving objects-changes continuously. Multidimensional database technology will increasingly be applied where analysis results are fed directly into other systems, thereby eliminating humans from the loop. When coupled with the need for continuous updates, this context poses stringent performance requirements not met by current technology.

SpaceTwist: Managing the Trade-Offs Among Location Privacy, Query Performance, and Query Accuracy in Mobile Services

In a mobile service scenario, users query a server for nearby points of interest but they may not want to disclose their locations to the service. Intuitively, location privacy may be obtained at the cost of query performance and query accuracy. The challenge addressed is how to obtain the best possible performance, subjected to given requirements for location privacy and query accuracy. Existing privacy solutions that use spatial cloaking employ complex server query processing techniques and entail the transmission of large quantities of intermediate result. Solutions that use transformation-based matching generally fall short in offering practical query accuracy guarantees. Our proposed framework, called SpaceTwist, rectifies these shortcomings for k nearest neighbor (kNN) queries. Starting with a location different from the users actual location, nearest neighbors are retrieved incrementally until the query is answered correctly by the mobile terminal. This approach is flexible, needs no trusted middleware, and requires only well-known incremental NN query processing on the server. The framework also includes a server-side granular search technique that exploits relaxed query accuracy guarantees for obtaining better performance. The paper reports on empirical studies that elicit key properties of SpaceTwist and suggest that the framework offers very good performance and high privacy, at low communication cost.

Nearest neighbor and reverse nearest neighbor queries for moving objects

With the proliferation of wireless communications and the rapid advances in technologies for tracking the positions of continuously moving objects, algorithms for efficiently answering queries about large numbers of moving objects increasingly are needed. One such query is the reverse nearest neighbor (RNN) query that returns the objects that have a query object as their closest object. While algorithms have been proposed that compute RNN queries for non-moving objects, there have been no proposals for answering RNN queries for continuously moving objects. Another such query is the nearest neighbor (NN) query, which has been studied extensively and in many contexts. Like the RNN query, the NN query has not been explored for moving query and data points. This paper proposes an algorithm for answering RNN queries for continuously moving points in the plane. As a part of the solution to this problem and as a separate contribution, an algorithm for answering NN queries for continuously moving points is also proposed. The results of performance experiments are reported.

Temporal data management

A wide range of database applications manage time-varying information. Existing database technology currently provides little support for managing such data. The research area of temporal databases has made important contributions in characterizing the semantics of such information and in providing expressive and efficient means to model, store, and query temporal data. This paper introduces the reader to temporal data management, surveys stale-of-the-art solutions to challenging aspects of temporal data management, and points to research directions.