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45
On Indexing Mobile Objects
, 1999
"... We show how to index mobile objects in one and two dimensions using efficient dynamic external memory data structures. The problem is motivated by real life applications in traffic monitoring, intelligent navigation and mobile communications domains. For the 1dimensional case, we give (i) a dynamic ..."
Abstract

Cited by 200 (14 self)
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We show how to index mobile objects in one and two dimensions using efficient dynamic external memory data structures. The problem is motivated by real life applications in traffic monitoring, intelligent navigation and mobile communications domains. For the 1dimensional case, we give (i) a dynamic, external memory algorithm with guaranteed worst case performance and linear space and (ii) a practical approximation algorithm also in the dynamic, external memory setting, which has linear space and expected logarithmic query time. We also give an algorithm with guaranteed logarithmic query time for a restricted version of the problem. We present extensions of our techniques to two dimensions. In addition we give a lower bound on the number of I/O's needed to answer the ddimensional problem. Initial experimental results and comparisons to traditional indexing approaches are also included. 1 Introduction Traditional database management systems assume that data stored in the database rem...
Indexing moving points
, 2003
"... We propose three indexing schemes for storing a set S of N points in the plane, each moving along a linear trajectory, so that any query of the following form can be answered quickly: Given a rectangle R and a real value t; report all K points of S that lie inside R at time t: We first present an in ..."
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Cited by 168 (13 self)
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We propose three indexing schemes for storing a set S of N points in the plane, each moving along a linear trajectory, so that any query of the following form can be answered quickly: Given a rectangle R and a real value t; report all K points of S that lie inside R at time t: We first present an indexing structure that, for any given constant e> 0; uses OðN=BÞ disk blocks and answers a query in OððN=BÞ 1=2þe þ K=BÞ I/Os, where B is the block size. It can also report all the points of S that lie inside R during a given time interval. A point can be inserted or deleted, or the trajectory of a point can be changed, in Oðlog 2 B NÞ I/Os. Next, we present a general approach that improves the query time if the queries arrive in chronological order, by allowing the index to evolve over time. We obtain a tradeoff between the query time and the number of times the index needs to be updated as the points move. We also describe an indexing scheme in which the number of I/Os required to answer a query depends monotonically on the difference between the query time stamp t and the current time. Finally, we develop an efficient indexing scheme to answer approximate
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 145 (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.
Query indexing and velocity constrained indexing: Scalable techniques for continuous queries on moving objects
 IEEE Transaction Computers
, 2002
"... Moving object environments are characterized by large numbers of moving objects and numerous concurrent continuous queries over these objects. Efficient evaluation of these queries in response to the movement of the objects is critical for supporting acceptable response times. In such environments t ..."
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Cited by 119 (19 self)
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Moving object environments are characterized by large numbers of moving objects and numerous concurrent continuous queries over these objects. Efficient evaluation of these queries in response to the movement of the objects is critical for supporting acceptable response times. In such environments the traditional approach of building an index on the objects (data) suffers from the need for frequent updates and thereby results in poor performance. In fact, a brute force, noindex strategy yields better performance in many cases. Neither the traditional approach, nor the brute force strategy achieve reasonable query processing times. This paper develops novel techniques for the efficient and scalable evaluation of multiple continuous queries on moving objects. Our solution leverages two complimentary techniques: Query Indexing and Velocity Constrained Indexing (VCI). Query Indexing relies on i) incremental evaluation; ii) reversing the role of queries and data; and iii) exploiting the relative locations of objects and queries. VCI takes advantage of the maximum possible speed of objects in order to delay the expensive operation of updating an index to reflect the movement of objects. In contrast to an earlier technique [29] that requires exact knowledge about the movement of the objects, VCI does not rely on such information. While Query Indexing outperforms VCI, it does not efficiently handle the arrival of new queries. Velocity constrained indexing, on the other hand, is unaffected by changes in queries. We demonstrate that a combination of Query Indexing and Velocity Constrained Indexing enables the scalable execution of insertion and deletion of queries in addition
Locating Objects in Mobile Computing
, 2001
"... In current distributed systems, the notion of mobility is emerging in many forms and applications. ..."
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Cited by 84 (6 self)
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In current distributed systems, the notion of mobility is emerging in many forms and applications.
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 81 (36 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.
STRIPES: An Efficient Index for Predicted Trajectories
 in SIGMOD
, 2004
"... Moving object databases are required to support queries on a large number of continuously moving objects. A key requirement for indexing methods in this domain is to efficiently support both update and query operations. Previous work on indexing such databases can be broadly divided into two categor ..."
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Cited by 66 (0 self)
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Moving object databases are required to support queries on a large number of continuously moving objects. A key requirement for indexing methods in this domain is to efficiently support both update and query operations. Previous work on indexing such databases can be broadly divided into two categories: indexing the past positions and indexing the future predicted positions. In this paper we focus on an efficient indexing method for indexing the future positions of moving objects. In this paper we propose an indexing method, called STRIPES, which indexes predicted trajectories in a dual transformed space. Trajectories for objects in ddimensional space become points in a higherdimensional 2dspace. This dual transformed space is then indexed using a regular hierarchical grid decomposition indexing structure. STRIPES can evaluate a range of queries including timeslice, window, and moving queries. We have carried out extensive experimental evaluation comparing the performance of STRIPES with the best known existing predicted trajectory index (the TPR*tree), and show that our approach is significantly faster than TPR*tree for both updates and search queries. 1.
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 59 (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...
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 58 (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.
Prediction and indexing of moving objects with unknown motion patterns
 In SIGMOD
, 2004
"... predicted time 2 at positions predicted time 1 at ..."