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54
The TPR*Tree: An Optimized SpatioTemporal Access Method for Predictive Queries
 In VLDB
, 2003
"... A predictive spatiotemporal query retrieves the set of moving objects that will intersect a query window during a future time interval. Currently, the only access method for processing such queries in practice is the TPRtree. In this paper we first perform an analysis to determine the factor ..."
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Cited by 190 (10 self)
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A predictive spatiotemporal query retrieves the set of moving objects that will intersect a query window during a future time interval. Currently, the only access method for processing such queries in practice is the TPRtree. In this paper we first perform an analysis to determine the factors that affect the performance of predictive queries and show that several of these factors are not considered by the TPRtree, which uses the insertion/deletion algorithms of the R*tree designed for static data. Motivated by this, we propose a new index structure called the TPR* tree, which takes into account the unique features of dynamic objects through a set of improved construction algorithms. In addition, we provide cost models that determine the optimal performance achievable by any datapartition spatiotemporal access method. Using experimental comparison, we illustrate that the TPR*tree is nearlyoptimal and significantly outperforms the TPRtree under all conditions.
Indexing SpatioTemporal Trajectories with Chebyshev Polynomials
 Proc. 2004 SIGMOD, toappear
"... In this thesis, we investigate the subject of indexing large collections of spatiotemporal trajectories for similarity matching. Our proposed technique is to first mitigate the dimensionality curse problem by approximating each trajectory with a low order polynomiallike curve, and then incorporate ..."
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Cited by 79 (0 self)
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In this thesis, we investigate the subject of indexing large collections of spatiotemporal trajectories for similarity matching. Our proposed technique is to first mitigate the dimensionality curse problem by approximating each trajectory with a low order polynomiallike curve, and then incorporate a multidimensional index into the reduced space of polynomial coefficients. There are many possible ways to choose the polynomial, including Fourier transforms, splines, nonlinear regressions, etc. Some of these possibilities have indeed been studied before. We hypothesize that one of the best approaches is the polynomial that minimizes the maximum deviation from the true value, which is called the minimax polynomial. Minimax approximation is particularly meaningful for indexing because in a branchandbound search (i.e., for finding nearest neighbours), the smaller the maximum deviation, the more pruning opportunities there exist. In general, among all the polynomials of the same degree, the optimal minimax polynomial is very hard to compute. However, it has been shown that the Chebyshev approximation is almost identical to the optimal minimax polynomial, and is easy to compute [32]. Thus, we shall explore how to use
Efficient Indexing of Spatiotemporal Objects
, 2002
"... Spatiotemporal objects, i.e., objects which change their position and/or extent over time appear in many applications. In this paper we examine the problem of indexing large volumes of such data. Important in this environment is how the spatiotemporal objects move and/or change. We consider a rath ..."
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Cited by 71 (11 self)
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Spatiotemporal objects, i.e., objects which change their position and/or extent over time appear in many applications. In this paper we examine the problem of indexing large volumes of such data. Important in this environment is how the spatiotemporal objects move and/or change. We consider a rather general case where object movements/changes are defined by combinations of polynomial functions. We further concentrate on "snapshot" as well as small "interval" queries as these are quite common when examining the history of the gathered data. The obvious approach that approximates each spatiotemporal object by an MBR and uses a traditional multidimensional access method to index them is inefficient. Objects that "live" for long time intervals have large MBRs which introduce a lot of empty space. Clustering long intervals has been dealt in temporal databases by the use of partially persistent indices. What differentiates this problem from traditional temporal indexing, is that objects are allowed to move/change during their lifetime. Better ways are thus needed to approximate general spatiotemporal objects. One obvious solution is to introduce artificial splits: the lifetime of a longlived object is split into smaller consecutive pieces. This decreases the empty space but increases the number of indexed MBRs. We first give an optimal algorithm and a heuristic for splitting a given spatiotemporal object in a predefined number of pieces. Then, given an upper bound on the total number of possible splits, we present three algorithms that decide how the splits are distributed among all the objects so that the total empty space is minimized. The number of splits cannot be increased indefinitely since the extra objects will eventually affect query performance. Usi...
Spatiotemporal Access Methods
 IEEE Data Engineering Bulletin
, 2003
"... The rapid increase in spatiotemporal applications calls for new auxiliary indexing structures. A typical spatiotemporal application is one that tracks the behavior of moving objects through locationaware devices (e.g., GPS). Through the last decade, many spatiotemporal access methods are develop ..."
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Cited by 59 (7 self)
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The rapid increase in spatiotemporal applications calls for new auxiliary indexing structures. A typical spatiotemporal application is one that tracks the behavior of moving objects through locationaware devices (e.g., GPS). Through the last decade, many spatiotemporal access methods are developed. Spatiotemporal access methods focus on two orthogonal directions: (1) Indexing the past, (2) Indexing the current and predicted future positions. In this short survey, we classify spatiotemporal access methods for each direction based on their underlying structure with a brief discussion of future research directions.
Range Aggregate Processing in Spatial Databases
 TKDE
, 2004
"... Abstract—A range aggregate query returns summarized information about the points falling in a hyperrectangle (e.g., the total number of these points instead of their concrete ids). This paper studies spatial indexes that solve such queries efficiently and proposes the aggregate Pointtree (aPtree) ..."
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Cited by 40 (3 self)
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Abstract—A range aggregate query returns summarized information about the points falling in a hyperrectangle (e.g., the total number of these points instead of their concrete ids). This paper studies spatial indexes that solve such queries efficiently and proposes the aggregate Pointtree (aPtree), which achieves logarithmic cost to the data set cardinality (independently of the query size) for twodimensional data. The aPtree requires only small modifications to the popular multiversion structural framework and, thus, can be implemented and applied easily in practice. We also present models that accurately predict the space consumption and query cost of the aPtree and are therefore suitable for query optimization. Extensive experiments confirm that the proposed methods are efficient and practical. Index Terms—Database, spatial database, range queries, aggregation. 1
Indexing the Past, Present and Anticipated Future Positions of Moving Objects
, 2004
"... With the proliferation of wireless communications and geopositioning, eservices are envisioned that exploit the positions of a set of continuously moving users to provide contextaware functionality to each individual user. Because advances in disk capacities continue to outperform Moore's ..."
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Cited by 35 (2 self)
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With the proliferation of wireless communications and geopositioning, eservices are envisioned that exploit the positions of a set of continuously moving users to provide contextaware functionality to each individual user. Because advances in disk capacities continue to outperform Moore's Law, it becomes increasingly feasible to store online all the position information obtained from the moving eservice users. With the much slower advances in I/O speeds and many concurrent users, indexing techniques are of essence in this scenario. Past
Indexing of network constrained moving objects
 In Proc. of the 11th Intl. Symp. on Advances in Geographic Information Systems (ACMGIS
, 2003
"... With the proliferation of mobile computing, the ability to index efficiently the movements of mobile objects becomes important. Objects are typically seen as moving in twodimensional (x,y) space, which means that their movements across time may be embedded in the threedimensional (x,y,t) space. Fu ..."
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Cited by 33 (2 self)
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With the proliferation of mobile computing, the ability to index efficiently the movements of mobile objects becomes important. Objects are typically seen as moving in twodimensional (x,y) space, which means that their movements across time may be embedded in the threedimensional (x,y,t) space. Further, the movements are typically represented as trajectories, sequences of connected line segments. In certain cases, movement is restricted, and specifically in this paper, we aim at exploiting that movements occur in transportation networks to reduce the dimensionality of the data. Briefly, the idea is to reduce movements to occur in one spatial dimension. As a consequence, the movement data becomes twodimensional (x,t). The advantages of considering such lowerdimensional trajectories are the reduced overall size of the data and the lowerdimensional indexing challenge. Since offtheshelf database management systems typically do not offer higherdimensional indexing, this reduction in dimensionality allows us to use such DBMSes to store and index trajectories. Moreover, we argue that, given the right circumstances, indexing these dimensionalityreduced trajectories can be more efficient than using a threedimensional index. This hypothesis is verified by an experimental study that incorporates trajectories stemming from real and synthetic road networks.
Indexing Spatiotemporal Archives
 THE VLDB JOURNAL
"... Spatiotemporal objects — that is, objects that evolve over time — appear in many applications. Due to the nature of such applications, storing the evolution of objects through time in order to answer historical queries (queries that refer to past states of the evolution) requires a very large speci ..."
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Cited by 31 (4 self)
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Spatiotemporal objects — that is, objects that evolve over time — appear in many applications. Due to the nature of such applications, storing the evolution of objects through time in order to answer historical queries (queries that refer to past states of the evolution) requires a very large specialized database, what is termed in this article as a spatiotemporal archive. Efficient processing of historical queries on spatiotemporal archives requires equally sophisticated indexing schemes. Typical spatiotemporal indexing techniques represent the objects using minimum bounding regions (MBR) extended with a temporal dimension, which are then indexed using traditional multidimensional index structures. However, rough MBR approximations introduce excessive overlap between index nodes which deteriorates query performance. This article introduces a robust indexing scheme for answering spatiotemporal queries more efficiently. A number of algorithms and heuristics are elaborated, which can be used to preprocess a spatiotemporal archive in order to produce finer object approximations which, in combination with a multiversion index structure, will greatly improve query performance in comparison to the straightforward approaches. The proposed techniques introduce a queryefficiency vs. space tradeoff, that can help tune a structure according to available resources. Empirical observations for estimating the necessary amount of additional storage space required for improving query performance by a given factor are also provided. Moreover, heuristics for applying the proposed ideas in an online setting are discussed. Finally, a thorough experimental evaluation is conducted to show the merits of the proposed techniques.
Shapebased Similarity Query for Trajectory of Mobile Objects
 Proceedings of MDM
, 2003
"... Abstract. In this paper, we describe an efficient indexing method for a shapebased similarity search of the trajectory of dynamically changing locations of people and mobile objects. In order to manage trajectories in database systems, we define a data model of trajectories as directed lines in a s ..."
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Cited by 28 (2 self)
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Abstract. In this paper, we describe an efficient indexing method for a shapebased similarity search of the trajectory of dynamically changing locations of people and mobile objects. In order to manage trajectories in database systems, we define a data model of trajectories as directed lines in a space, and the similarity between trajectories is defined as the Euclidean distance between directed discrete lines. Our proposed similarity query can be used to find interested patterns embedded into the trajectories, for example, the trajectories of mobile cars in a city may include patterns for expecting traffic jams. Furthermore, we propose an efficient indexing method to retrieve similar trajectories for a query by combining a spatial indexing technique (R +Tree) and a dimension reduction technique, which is called PAA (Piecewise Approximate Aggregate). The indexing method can efficiently retrieve trajectories whose shape in a space is similar to the shape of a candidate trajectory from the database. 1
Historical spatiotemporal aggregation
 ACM Trans. Inf. Syst
, 2005
"... Spatiotemporal databases store information about the positions of individual objects over time. However, in many applications such as traffic supervision or mobile communication systems, only summarized data, like the number of cars in an area for a specific period, or phonecalls serviced by a cel ..."
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Cited by 23 (4 self)
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Spatiotemporal databases store information about the positions of individual objects over time. However, in many applications such as traffic supervision or mobile communication systems, only summarized data, like the number of cars in an area for a specific period, or phonecalls serviced by a cell each day, is required. Although this information can be obtained from operational databases, its computation is expensive, rendering online processing inapplicable. In this paper, we present specialized methods, which integrate spatiotemporal indexing with preaggregation. The methods support dynamic spatiotemporal dimensions for the efficient processing of historical aggregate queries without apriori knowledge of grouping hierarchies. The superiority of the proposed techniques over existing methods is demonstrated through a comprehensive probabilistic analysis and an extensive experimental evaluation.