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186
TimeParameterized Queries in SpatioTemporal Databases
, 2002
"... Timeparameterized queries (TP queries for short) retrieve (i) the actual result at the time that the query is issued, (ii) the validity period of the result given the current motion of the query and the database objects, and (iii) the change that causes the expiration of the result. Due to the hi ..."
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Cited by 84 (4 self)
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Timeparameterized queries (TP queries for short) retrieve (i) the actual result at the time that the query is issued, (ii) the validity period of the result given the current motion of the query and the database objects, and (iii) the change that causes the expiration of the result. Due to the highly dynamic nature of several spatiotemporal applications, TP queries are important both as standalone methods, as well as building blocks of more complex operations. However, little work has been done towards their efficient processing. In this paper, we propose a general framework that covers timeparameterized variations of the most common spatial queries, namely window queries, knearest neighbors and spatial joins. In particular, each of these TP queries is reduced to nearest neighbor search where the distance functions are def'med according to the query type. This reduction allows the application and extension of wellknown branch and bound techniques to the current problem. The proposed methods can be applied with mobile queries, mobile objects or both, given a suitable indexing method. Our experimental evaluation is based on Rtrees and their extensions for dynamic objects.
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
External Memory Data Structures
, 2001
"... In many massive dataset applications the data must be stored in space and query efficient data structures on external storage devices. Often the data needs to be changed dynamically. In this chapter we discuss recent advances in the development of provably worstcase efficient external memory dynami ..."
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Cited by 76 (32 self)
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In many massive dataset applications the data must be stored in space and query efficient data structures on external storage devices. Often the data needs to be changed dynamically. In this chapter we discuss recent advances in the development of provably worstcase efficient external memory dynamic data structures. We also briefly discuss some of the most popular external data structures used in practice.
Indexing Large Trajectory Data Sets With SETI
, 2003
"... With the rapid increase in the use of inexpensive, locationaware sensors in a variety of new applications, large amounts of timesequenced location data will soon be accumulated. Efficient indexing techniques for managing these large volumes of trajectory data sets are urgently needed. The key ..."
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Cited by 73 (2 self)
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With the rapid increase in the use of inexpensive, locationaware sensors in a variety of new applications, large amounts of timesequenced location data will soon be accumulated. Efficient indexing techniques for managing these large volumes of trajectory data sets are urgently needed. The key requirements for a good trajectory indexing technique is that it must support both searches and inserts efficiently.
Indexing the Current Positions of Moving Objects Using the Lazy Update RTree
 In Mobile Data Management, MDM
, 2002
"... With the rapid advances of wireless communications and positioning techniques, tracking the positions of moving objects is becoming increasingly feasible and necessary. Traditional spatial index structures are not suitable for storing these positions because of numerous update operations. To reduce ..."
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Cited by 73 (1 self)
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With the rapid advances of wireless communications and positioning techniques, tracking the positions of moving objects is becoming increasingly feasible and necessary. Traditional spatial index structures are not suitable for storing these positions because of numerous update operations. To reduce the number of update operations, many existing approaches use a linear function to describe the movements of objects. In many real applications, however, the movements of objects are too complicated to be represented as a simple linear function. In this case, such approaches based on a linear function cannot reduce update cost efficiently. In this paper, we propose a novel Rtree based indexing technique called LURtree. This technique updates the structure of the index only when an object moves out of the corresponding MBR (minimum bounding rectangle). If a new position of an object is in the MBR, it changes only the position of the object in the leaf node. It can update the position of the object quickly and reduce update cost greatly. Since it is based on the Rtree, the LURtree also uses the same algorithms to process various types of queries as the Rtree. We present the experimental results which show that our technique outperforms other techniques 1.
Range Searching
, 1996
"... Range searching is one of the central problems in computational geometry, because it arises in many applications and a wide variety of geometric problems can be formulated as a rangesearching problem. A typical rangesearching problem has the following form. Let S be a set of n points in R d , an ..."
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Cited by 73 (1 self)
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Range searching is one of the central problems in computational geometry, because it arises in many applications and a wide variety of geometric problems can be formulated as a rangesearching problem. A typical rangesearching problem has the following form. Let S be a set of n points in R d , and let R be a family of subsets; elements of R are called ranges . We wish to preprocess S into a data structure so that for a query range R, the points in S " R can be reported or counted efficiently. Typical examples of ranges include rectangles, halfspaces, simplices, and balls. If we are only interested in answering a single query, it can be done in linear time, using linear space, by simply checking for each point p 2 S whether p lies in the query range.
Prediction and indexing of moving objects with unknown motion patterns
 In SIGMOD
, 2004
"... predicted time 2 at positions predicted time 1 at ..."
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...
Never walk alone: Uncertainty for anonymity in moving objects databases
 In ICDE
, 2008
"... Abstract — Preserving individual privacy when publishing data is a problem that is receiving increasing attention. According to the kanonymity principle, each release of data must be such that each individual is indistinguishable from at least k −1 other individuals. In this paper we study the prob ..."
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Cited by 70 (5 self)
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Abstract — Preserving individual privacy when publishing data is a problem that is receiving increasing attention. According to the kanonymity principle, each release of data must be such that each individual is indistinguishable from at least k −1 other individuals. In this paper we study the problem of anonymity preserving data publishing in moving objects databases. We propose a novel concept of kanonymity based on colocalization that exploits the inherent uncertainty of the moving object’s whereabouts. Due to sampling and positioning systems (e.g., GPS) imprecision, the trajectory of a moving object is no longer a polyline in a threedimensional space, instead it is a cylindrical volume, where its radius δ represents the possible location imprecision: we know that the trajectory of the moving object is within this cylinder, but we do not know exactly where. If another object moves within the same cylinder they are indistinguishable from each other. This leads to the definition of (k, δ)anonymity for moving objects databases. We first characterize the (k, δ)anonymity problem and discuss techniques to solve it. Then we focus on the most promising technique by the point of view of information preservation, namely space translation. We develop a suitable measure of the information distortion introduced by space translation, and we prove that the problem of achieving (k, δ)anonymity by space translation with minimum distortion is NPhard. Faced with the hardness of our problem we propose a greedy algorithm based on clustering and enhanced with ad hoc preprocessing and outlier removal techniques. The resulting method, named N WA (N ever Walk Alone), is empirically evaluated in terms of data quality and efficiency. Data quality is assessed both by means of objective measures of information distortion, and by comparing the results of the same spatiotemporal range queries executed on the original database and on the (k, δ)anonymized one. Experimental results show that for a wide range of values of δ and k, the relative error introduced is kept low, confirming that N WA produces high quality (k, δ)anonymized data.
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.