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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.
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.
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.
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 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.
2012
The proliferation of devices able to monitor their position is favoring the accumulation of large amount of geographically referenced data, that can be profitably used in a lot of applications, ranging from traffic control and management to location-aware services. The strong interest in these applications has entailed a significant research effort in the last years, both toward the modeling of spatio-temporal databases and toward indexing strategies to efficiently process spatio-temporal queries. Recently, we presented an indexing scheme (based on a redundant storing strategy) able to index three-dimensional trajectories using widely available bidimensional indexes. In this paper we propose a method that, while avoids redundant storing of data, still uses well established bi-dimensional indexes. With respect to the previous work, the retrieving performance is improved by taking advantage both of a more efficient representation and of a trajectory segmentation stage, as experimental results show.
Distributed and Parallel Databases, 2005
We consider the problem of indexing a set of objects moving in d-dimensional spaces along linear trajectories. A simple external-memory indexing scheme is proposed to efficiently answer general range queries. The following are examples of the queries that can be answered by the proposed method: report all moving objects that will (i) pass between two given points within a specified time interval; (ii) become within a given distance from some or all of a given set of other moving objects. Our scheme is based on mapping the objects to a dual space, where queries about moving objects are transformed 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 guarantee an average search time that 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
2008
The widespread diffusion of modern technologies such as low-cost sensors, wireless, ubiquitous and location-aware mobile devices, allows one to collect an overwhelming amount of data about trajectories of moving objects. Such data are usually produced at different rates, and arrive in streams in an unpredictable and unbounded way.
The widespread diffusion of modern technologies such as low-cost sensors, wireless, ubiquitous and location-aware mobile devices, allows one to collect an overwhelming amount of data about trajectories of moving objects. Such data are usually produced at different rates, and arrive in streams in an unpredictable and unbounded way.
Eighth International Conference on Database Systems for Advanced Applications, 2003. (DASFAA 2003). Proceedings., 2003
Moving object environments contain large numbers of queries and continuously moving objects. Traditional spatial index structures do not work well in this environment because of the need to frequently update the index which results in very poor performance. In this paper, we present a novel indexing structure, namely the Q+Rtree, based on the observation that i) most moving objects are in quasi-static state most of time, and ii) the moving patterns of objects are strongly related to the topography of the space. The Q+Rtree is a hybrid tree structure which consists of both an R-tree and a QuadTree. The Rtree component indexes quasi-static objects-those that are currently moving slowly and are often crowded together in buildings or houses. The Quadtree component indexes fast moving objects which are dispersed over wider regions. We also present the experimental evaluation of our approach.
Computing in Science and Engineering, 2007
In this paper we investigate some issues and solutions related to the design of a Data Warehouse (DW), storing several aggregate measures about trajectories of moving objects. First we discuss the loading phase of our DW which has to deal with overwhelming streams of trajectory observations, possibly produced at different rates, and arriving in an unpredictable and unbounded way. Then, we focus on the measure presence, the most complex measure stored in our DW. Such a measure returns the number of distinct trajectories that lie in a spatial region during a given temporal interval. We devise a novel way to compute an approximate, but very accurate, presence aggregate function, which algebraically combines a bounded amount of measures stored in the base cells of the data cube.
Computers, Environment and Urban Systems, 2018
With the dramatic development of location-based services, a large amount of vehicle trajectory data are available and applied to different areas, while there are still many research challenges left, one of them being data access issues. Most of existing tree-shape indexing schemes cannot facilitate maintenance and management of very large vehicle trajectory data. How to retrieve vehicle trajectory information efficiently requires more efforts. Accordingly, this paper presents a trip-oriented data indexing scheme, named TripCube, for massive vehicle trajectory data. Its principle is to represent vehicle trajectory data as trip information records and develop a three-dimensional cube-shape indexing structure to achieve trip-oriented trajectory data retrieval. In particular, the approach is implemented and applied to vehicle trajectory data in the city of Shanghai including N100 million locational records per day collected from about 13,000 taxis. TripCube is compared to two existing trajectory data indexing structures in our experiments, and the result exhibits that TripCube outperforms others.
The domain of spatiotemporal applications is a treasure trove of new types of data and queries. However, work in this area is guided by related research from the spatial and temporal domains, so far, with little attention towards the true nature of spatiotemporal phenomena. In this work, the focus is on a spatiotemporal sub-domain, namely the trajectories of moving point objects. We present new types of spatiotemporal queries, as well as algorithms to process those. Further, we introduce two access methods this kind of data, namely the Spatio-Temporal R-tree (STR-tree) and the Trajectory-Bundle tree (TB-tree). The former is an R-tree based access method that considers the trajectory identity in the index as well, while the latter is a hybrid structure, which preserves trajectories as well as allows for R-tree typical range search in the data. We present performance studies that compare the two indices with the R-tree (appropriately modified, for a fair comparison) under a varying set of spatiotemporal queries, and we provide guidelines for a successful choice among them.
2008
Technological advances in sensing technologies and wireless telecommunication devices enable novel research fields related to the management of trajectory data. As it usually happens in data management world, the challenge after storing the data is the implementation of appropriate analytics that could extract useful knowledge. However, traditional data warehousing systems and techniques were not designed for analyzing trajectory data. Thus, in this work, we investigate how the traditional data cube model is adapted to trajectory warehouses in order to transform raw location data into valuable information. In particular, we focus our research on three issues that are critical to trajectory data warehousing: (a) the trajectory reconstruction procedure that takes place in order to transform sampled location data originated e.g. from GPS recordings into trajectories and load them to a moving object database, (b) the ETL procedure that feeds a trajectory data warehouse, and (c) the aggregation of cube measures for OLAP purposes. We provide design solutions for all these issues and we test their applicability and efficiency in real world settings.
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.
New Trends in Data Warehousing and Data Analysis, 2009
The study of moving objects has been capturing the attention of Geographic Information System (GIS) researchers. Moving objects, carrying location-aware devices, produce trajectory data in the form of a sample of (O id , t, x, y)-tuples, that contain object identifier and time-space information. Recently, the notion of stops and moves was introduced. Intuitively, if a moving object spends a sufficient amount of time in a certain geographic place (which we denote a place of interest of an application), this place is considered a stop of the object's trajectory. In-between stops, a trajectory has moves. In this paper we study how moving object data analysis can benefit from replacing raw trajectory data by a sequence of stops and moves. We first propose a formal model and query language (denoted L mo ) to express complex queries involving spatial data stored in a GIS, non-spatial data (stored in a data warehouse) and moving object data. This query language also supports different forms of aggregation. We then study the compression of trajectory data produced by moving objects, using the concepts of stops and moves. We show that stops and moves are expressible in L mo and that there exists a fragment of this language (that can be expressed by means of regular expressions) allowing to talk about temporally ordered sequences of stops and moves. We use this fragment to perform data mining over trajectory data. We present an implementation and a case study, and discuss different applications of our approach.
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.
Proceedings of the International Workshop on Temporal Representation and Reasoning, 2007
Trajectory Database (TD) management is a relatively new topic of database research, which has emerged due to the explosion of mobile devices and positioning technologies. Trajectory similarity search forms an important class of queries in TD with applications in trajectory data analysis and spatiotemporal knowledge discovery. In contrast to related works which make use of generic similarity metrics that virtually ignore the temporal dimension, in this paper we introduce a framework consisting of a set of distance operators based on primitive (space and time) as well as derived parameters of trajectories (speed and direction). The novelty of the approach is not only to provide qualitatively different means to query for similar trajectories, but also to support trajectory clustering and classification mining tasks, which definitely imply a way to quantify the distance between two trajectories. For each of the proposed distance operators we devise highly parametric algorithms, the efficiency of which is evaluated through an extensive experimental study using synthetic and real trajectory datasets.
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
International Journal of Computing and Business Research
The usage of location aware devices, such as mobile phones and GPS-enabled devices, is widely spread nowadays, allowing access to large spatiotemporal datasets. The space-time nature of this kind of data results in the generation of huge amounts of trajectory data and imposes new challenges regarding their efficient management. To address this need, the traditional database technology has been extended into Moving Object Databases (MODs) that handle modeling, indexing and query processing issues for trajectories. Moreover, the analysis of such trajectory data raises opportunities for discovering behavioral patterns that can be exploited in applications like traffic management and service accessibility. Online analytical processing (OLAP) and data mining (DM) techniques have been employed in order to convert this vast amount of raw data into useful knowledge. Indicatively, the variable number of moving objects in different urban areas, the average speed of vehicles, the ups and downs of vehicles speed as well as useful insights, like discovering popular movements can be analyzed in a Trajectory Data Warehouse (TDW).
The prosperity of mobile social network and location-based services, e.g., Uber, is backing the explosive growth of spatial temporal streams on the Internet. It raises new challenges to the underlying data store system, which is supposed to support extremely high-throughput trajectory insertion and low-latency querying with spatial and temporal constraints. State-of-the-art solutions, e.g., HBase, do not render satisfactory performance, due to the high overhead on index update. In this demonstration, we present DITIR, our new system prototype tailored to efficiently processing temporal and spacial queries over historical data as well as latest updates. Our system provides better performance guarantee, by physically partitioning the incoming data tuples on their arrivals and exploiting a template-based insertion schema, to reach the desired ingestion throughput. Load balancing mechanism is also introduced to DITIR, by using which the system is capable of achieving reliable performance against workload dynamics. Our demonstration shows that DITIR supports over 1 million tuple insertions in a second, when running on a 10-node cluster. It also significantly outper-forms HBase by 7 times on ingestion throughput and 5 times faster on query latency.
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