Close pair queries in moving object databases

Lecture Notes in Computer Science, 2005

Many new applications involving moving objects require the collection and querying of trajectory data, so efficient indexing methods are needed to support complex spatio-temporal queries on such data. Current work in this domain has used MBRs to approximate trajectories, which fail to capture some basic properties of trajectories, including smoothness and lack of internal area. This mismatch leads to poor pruning when such indices are used. In this work, we revisit the issue of using parametric space indexing for historical trajectory data. We approximate a sequence of movement functions with single continuous polynomial. Since trajectories tend to be smooth, our approximations work well and yield much finer approximation quality than MBRs. We present the PA-tree, a parametric index that uses this new approximation method. Experiments show that PA-tree construction costs are orders of magnitude lower than that of competing methods. Further, for spatio-temporal range queries, MBR-based methods require 20%-60% more I/O than PA-trees with clustered indicies, and 300%-400% more I/O than PA-trees with non-clustered indicies.

Proceedings of the 6th international conference on Mobile data management, 2005

Although significant effort has been put into the development of efficient spatio-temporal indexing techniques for moving objects, little attention has been given to the development of techniques that efficiently support queries about the past, present, and future positions of objects. The provisioning of such techniques is challenging, both because of the nature of the data, which reflects continuous movement, and because of the types of queries to be supported. This paper proposes the BB x-index structure, which indexes the positions of moving objects, given as linear functions of time, at any time. The index stores linearized moving-object locations in a forest of B +-trees. The index supports queries that select objects based on temporal and spatial constraints, such as queries that retrieve all objects whose positions fall within a spatial range during a set of time intervals. Empirical experiments are reported that offer insight into the query and update performance of the proposed technique.

The VLDB Journal, 2006

With the continued proliferation of wireless communications and advances in positioning technologies, algorithms for efficiently answering queries about large populations of moving objects are gaining interest. This paper proposes algorithms for k nearest and reverse k nearest neighbor queries on the current and anticipated future positions of points moving continuously in the plane. The former type of query returns k objects nearest to a query object for each time point during a time interval, while the latter returns the objects that have a specified query object as one of their k closest neighbors, again for each time point during a time interval. In addition, algorithms for so-called persistent and continuous variants of these queries are provided. The algorithms are based on the indexing of object positions represented as linear functions of time. The results of empirical performance experiments are reported.

Lecture Notes in Computer Science, 2005

Nearest Neighbor (NN) search has been in the core of spatial and spatiotemporal database research during the last decade. The literature on NN query processing algorithms so far deals with either stationary or moving query points over static datasets or future (predicted) locations over a set of continuously moving points. With the increasing number of Mobile Location Services (MLS), the need for effective k-NN query processing over historical trajectory data has become the vehicle for data analysis, thus improving existing or even proposing new services.

Geographic Information Science …, 2009

Lecture Notes in Computer Science, 2002

We consider the problem of indexing a set of objects moving in d-dimensional space along linear trajectories. A simple disk-based indexing scheme is proposed to efficiently answer queries of the form: report all objects that will pass between two given points within a specified time interval. Our scheme is based on mapping the objects to a dual space, where queries about moving objects translate into polyhedral queries concerning their speeds and initial locations. We then present a simple method for answering such polyhedral queries, based on partitioning the space into disjoint regions and using a B-tree to index the points in each region. By appropriately selecting the boundaries of each region, we can guarantee an average search time that almost matches a known lower bound for the problem. Specifically, for a fixed d, if the coordinates of a given set of N points are statistically independent, the proposed technique answers polyhedral queries, on the average, in

Proceedings of the 22nd ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems - SIGSPATIAL '14, 2014

The plethora of lacation-aware devices has led to countless locationbased services in which huge amounts of spatio-temporal data get created everyday. Several applications requie efficient processing of queries on the locations of moving objects over time, i.e., the moving object trajectories. This calls for efficient trajectory-based indexing methods that capture both the spatial and temporal dimensions of the data in a way that minimizes the number of disk I/Os required for both updating and querying. Motivated by applications that require only the recent history of a moving object's trajectory, this paper introduces the trails-tree; a disk-based data structure for indexing recent trajectories. The trails-tree maintains a temporalsliding window over the trajectories and uses: (1) an in-memory memo structure that reduces the I/O cost of updates using a lazyupdate mechanism, and (2) a lazy vacuum-cleaning mechanism to delete parts of the trajectories that fall out of the sliding window. Experimental evaluation illustrates that the trails-tree outperforms the state-of-the-art index structures for indexing recent trajectory data by up to a factor of two.

Proceedings of the 15th annual ACM international symposium on Advances in geographic information systems - GIS '07, 2007

The increasingly popular GPS technology and the growing amount of trajectory data it generates create the need for developing applications that efficiently store and query trajectories of moving objects. In this paper we introduce TS2 tree, a novel indexing structure for organizing trajectory data based on similarity between trajectories. TS2 tree provides lower and upper bounds on distance between trajectories, based on which we propose a general framework for effectively answering a wide range of similarity-based trajectory queries such as similarity threshold (ST) query and similarity best fit (SBF) query. The multifold reduction in query computation times and the number of I/O operations is demonstrated through an extensive experimental evaluation.

Theoretical Computer Science, 2005

Given a set of n objects, each characterized by d attributes speci ed at m xed time instances, we are interested in the problem of designing space e cient indexing structures such that arbitrary temporal range search queries can be handled e ciently. When m = 1, our problem reduces to the d-dimensional orthogonal search problem. We establish e cient data structures to handle several classes of the general problem. Our results include a linear size data structure that enables a query time of O(log n log m= log log n + f) for one-sided queries when d = 1, where f is the number of objects satisfying the query. A similar result is shown for counting queries. We also show that the most general problem can be solved with a polylogarithmic query time using nonlinear space data structures.

2010

A trajectory is defined as the record of time-varying spatial phenomenon. The trajectory database is an important research area that has received a lot of interest in the last decade, with the objective of trajectory databases being to extend existing database technology to support the representation and querying of moving objects and their trajectories. Querying in trajectory databases can be very expensive due to the nature of the data and the complexity of the query processing algorithms. Given also that location-aware devices, like the GPS, are present everywhere these days, trajectory databases will soon face an enormous amount of data. Consequently the performance in the presence of a vast amount of data will be a significant problem and efficient indexing schemes are required to support both updates and searches efficiently. This paper provides the methodology for using the recursive partitioning technique for indexing trajectories in the unrestricted space, which is called the Recursively Partitioned Trajectory Index (RPTI). RPTI uses the two-level indexing structure, as does the state of art indexing scheme, SETI, and maintains separate indices for the space and time dimensions. We present the algorithms for constructing the RPTI and the algorithms for updates that include insertion and deletion. We also provide the results of the experimental study on the RPTI and have demonstrated that RPTI is better than SETI in handling trajectory-based queries and is competitive with SETI in handling coordinate-based queries. The structure of RPTI can be easily implemented by using any of the existing spatial indexing structures. The only design parameters required are the standard disk page size and maximum level of recursive partitioning.

IEEE Transactions on Knowledge and Data Engineering, 2007

Complex queries on trajectory data are increasingly common in applications involving moving objects. MBR or grid-cell approximations on trajectories perform suboptimally since they do not capture the smoothness and lack of internal area of trajectories. We describe a parametric space indexing method for historical trajectory data, approximating a sequence of movement functions with single continuous polynomial. Our approach works well, yielding much finer approximation quality than MBRs. We present the PA-tree, a parametric index that uses this method, and show through extensive experiments that PA-trees have excellent performance for offline and online spatio-temporal range queries. Compared to MVR-trees, PA-trees are an order of magnitude faster to construct and incur I/O cost for spatio-temporal range queries lower by a factor of 2-4. SETI is faster than our method for index construction and timestamp queries, but incurs twice the I/O cost for time interval queries, which are much more expensive and are the bottleneck in online processing. Therefore, the PA-tree is an excellent choice for both offline and online processing of historical trajectories.

Proceedings of the twenty-first ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems - PODS '02, 2002

Database applications for moving objects pose new challenges in modeling, querying, and maintenance of objects whose locations are rapidly changing over time. Previous work on modeling and querying spatio-temporal databases and constraint databases focus primarily on snapshots of changing databases. In this paper we study query evaluation techniques for moving object databases where moving objects are being updated frequently. We consider a constraint database approach to moving objects and queries. We classify moving object queries into: "past", "continuing", and "future" queries. We argue that while traditional constraint query evaluation techniques are suitable for past queries, new techniques are needed for continuing and future queries. Motivated by nearest-neighbor queries, we define a query language based on a single "generalized distance" function f mapping from objects to continuous functions from time to R. Queries in this language may be past, continuing, or future. We show that if f maps to polynomials, queries can be evaluated efficiently using the plane sweeping technique from computational geometry. Consequently, many known distance based queries can be evaluated efficiently.

Lecture Notes in Computer Science, 2004

The ability to represent and query continuously moving objects is important in many applications of spatio-temporal database systems. In this paper we develop data structures for answering various queries on moving objects, including range and proximity queries, and study tradeoffs between various performance measures-query time, data structure size, and accuracy of results.

2011

Sensors, 2014

In recent years, there has been tremendous growth in the field of indoor and outdoor positioning sensors continuously producing huge volumes of trajectory data that has been used in many fields such as location-based services or location intelligence. Trajectory data is massively increased and semantically complicated, which poses a great challenge on spatio-temporal data indexing. This paper proposes a spatio-temporal data indexing method, named HBSTR-tree, which is a hybrid index structure comprising spatio-temporal R-tree, B*-tree and Hash table. To improve the index generation efficiency, rather than directly inserting trajectory points, we group consecutive trajectory points as nodes according to their spatio-temporal semantics and then insert them into spatio-temporal R-tree as leaf nodes. Hash table is used to manage the latest leaf nodes to reduce the frequency of insertion. A new spatio-temporal interval criterion and a new node-choosing sub-algorithm are also proposed to optimize spatio-temporal R-tree structures. In addition, a B*-tree sub-index of leaf nodes is built to query the trajectories of targeted objects efficiently. Furthermore, a database storage scheme based on a NoSQL-type DBMS is also proposed for the purpose of cloud storage. Experimental results prove that HBSTR-tree outperforms TB*-tree in some aspects such as generation efficiency, query performance and query type.