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166
Indexing the Positions of Continuously Moving Objects
, 2000
"... The coming years will witness dramatic advances in wireless communications as well as positioning technologies. As a result, tracking the changing positions of objects capable of continuous movement is becoming increasingly feasible and necessary. The present paper proposes a novel, R # tree base ..."
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Cited by 317 (18 self)
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The coming years will witness dramatic advances in wireless communications as well as positioning technologies. As a result, tracking the changing positions of objects capable of continuous movement is becoming increasingly feasible and necessary. The present paper proposes a novel, R # tree based indexing technique that supports the efficient querying of the current and projected future positions of such moving objects. The technique is capable of indexing objects moving in one, two, and threedimensional space. Update algorithms enable the index to accommodate a dynamic data set, where objects may appear and disappear, and where changes occur in the anticipated positions of existing objects. A comprehensive performance study is reported.
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 ..."
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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.
Discrete Mobile Centers
 Discrete and Computational Geometry
, 2001
"... We propose a new randomized algorithm for maintaining a set of clusters among moving nodes in the plane. Given a specified cluster radius, our algorithm selects and maintains a variable subset of the nodes as cluster centers. This subset has the property that (1) balls of the given radius centered a ..."
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Cited by 97 (15 self)
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We propose a new randomized algorithm for maintaining a set of clusters among moving nodes in the plane. Given a specified cluster radius, our algorithm selects and maintains a variable subset of the nodes as cluster centers. This subset has the property that (1) balls of the given radius centered at the chosen nodes cover all the others and (2) the number of centers selected is a constantfactor approximation of the minimum possible. As the nodes move, an eventbased kinetic data structure updates the clustering as necessary. This kinetic data structure is shown to be responsive, efficient, local, and compact. The produced cover is also smooth, in the sense that wholesale cluster rearrangements are avoided. The algorithm can be implemented without exact knowledge of the node positions, if each node is able to sense its distance to other nodes up to the cluster radius. Such a kinetic clustering can be used in numerous applications where mobile devices must be interconnected into an adhoc network to collaboratively perform some tasks. 1
Approximating extent measure of points
 Journal of ACM
"... We present a general technique for approximating various descriptors of the extent of a set of points in�when the dimension�is an arbitrary fixed constant. For a given extent measure�and a parameter��, it computes in time a subset�of size, with the property that. The specific applications of our tec ..."
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Cited by 96 (28 self)
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We present a general technique for approximating various descriptors of the extent of a set of points in�when the dimension�is an arbitrary fixed constant. For a given extent measure�and a parameter��, it computes in time a subset�of size, with the property that. The specific applications of our technique include�approximation algorithms for (i) computing diameter, width, and smallest bounding box, ball, and cylinder of, (ii) maintaining all the previous measures for a set of moving points, and (iii) fitting spheres and cylinders through a point set. Our algorithms are considerably simpler, and faster in many cases, than previously known algorithms. 1
Kinetic Data Structures  A State of the Art Report
, 1998
"... ... In this paper we present a general framework for addressing such problems and the tools for designing and analyzing relevant algorithms, which we call kinetic data structures. We discuss kinetic data structures for a variety of fundamental geometric problems, such as the maintenance of convex hu ..."
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Cited by 92 (27 self)
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... In this paper we present a general framework for addressing such problems and the tools for designing and analyzing relevant algorithms, which we call kinetic data structures. We discuss kinetic data structures for a variety of fundamental geometric problems, such as the maintenance of convex hulls, Voronoi and Delaunay diagrams, closest pairs, and intersection and visibility problems. We also briefly address the issues that arise in implementing such structures robustly and efficiently. The resulting techniques satisfy three desirable properties: (1) they exploit the continuity of the motion of the objects to gain efficiency, (2) the number of events processed by the algorithms is close to the minimum necessary in the worst case, and (3) any object may change its `flight plan' at any moment with a low cost update to the simulation data structures. For computer applications dealing with motion in the physical world, kinetic data structures lead to simulation performance unattainable by other means. In addition, they raise fundamentally new combinatorial and algorithmic questions whose study may prove fruitful for other disciplines as well.
Indexing of Moving Objects for LocationBased Services
, 2001
"... With the continued proliferation of wireless networks, e.g., based on such evolving standards as WAP and Bluetooth, visionaries predict that the Internet will soon extend to billions of wireless devices, or objects. A substantial fraction of these will offer their changing positions to the (locati ..."
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Cited by 89 (15 self)
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With the continued proliferation of wireless networks, e.g., based on such evolving standards as WAP and Bluetooth, visionaries predict that the Internet will soon extend to billions of wireless devices, or objects. A substantial fraction of these will offer their changing positions to the (locationbased) services, they either use or support. As a result, software technologies that enable the management of the positions of objects capable of continuous movement are in increasingly high demand. This paper assumes what we consider a realistic Internetservice scenario where objects that have not reported their position within a specified duration of time are expected to no longer be interested in, or of interest to, the service. In this scenario, the possibility of substantial quantities of "expiring" objects introduces a new kind of implicit update, which contributes to rendering the database highly dynamic. The paper presents an Rtree based technique for the indexing of the current positions of such objects. Extensive performance experiments explore the properties of the types of bounding regions that are candidates for being used in the internal entries of the index, and they show that, when compared to the approach where the objects are not assumed to expire, the new indexing technique can improve the search performance by as much as a factor of two or more without sacrificing update performance.
Nearestneighbor searching and metric space dimensions
 In NearestNeighbor Methods for Learning and Vision: Theory and Practice
, 2006
"... Given a set S of n sites (points), and a distance measure d, the nearest neighbor searching problem is to build a data structure so that given a query point q, the site nearest to q can be found quickly. This paper gives a data structure for this problem; the data structure is built using the distan ..."
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Cited by 87 (0 self)
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Given a set S of n sites (points), and a distance measure d, the nearest neighbor searching problem is to build a data structure so that given a query point q, the site nearest to q can be found quickly. This paper gives a data structure for this problem; the data structure is built using the distance function as a “black box”. The structure is able to speed up nearest neighbor searching in a variety of settings, for example: points in lowdimensional or structured Euclidean space, strings under Hamming and edit distance, and bit vector data from an OCR application. The data structures are observed to need linear space, with a modest constant factor. The preprocessing time needed per site is observed to match the query time. The data structure can be viewed as an application of a “kdtree ” approach in the metric space setting, using Voronoi regions of a subset in place of axisaligned boxes. 1
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.