| P.K. Agarwal, L. Arge, J. Erickson: "Indexing Moving Points", Proceedings 19th ACM Symposium on Principles of Database Systems (PODS'2000), pp.175-186, Madison, WI, 2000. |
....due to the emergence and importance of location aware applications like intelligent traffic management, mobile communications, sensor based surveillance systems, etc. Typically the location of a moving object is represented as a function of time and the database stores the function parameters [2], 1] 17] 9] 22] 21] 16] 24] 15] 27] 23] 10] This results into a tractable update load. The system is updated only when an object changes any of its moving parameters (e.g. speed, direction, etc) The alternative of storing the object s continuously changing location is ....
....answer interesting queries about the locations of the moving objects in the future. Examples include range queries: Find which objects will be in area A, ten minutes from now [10] This work was partially supported by NSF grants IIS 9907477, EIA9983445, IIS 0220148 and Career Award 0133825. [2], 17] 9] 22] 21] 20] nearest neighbor queries: Find the closest object(s) to a given location within the next five minutes [24] etc. The answer to such queries is based on the knowledge about the object movements at the time the query is issued [25] 26] In this paper we present a ....
[Article contains additional citation context not shown here]
P. K. Agarwal, L. Arge, and J. Erickson. Indexing moving points. (PODS), pages 175--186, 2000.
....years due to the emergence and importance of location aware applications like intelligent trac management, mobile communications, sensor based surveillance systems, etc. Typically, the location of a moving object is represented as a function of time and the database stores the function parameters [2, 1, 17, 9, 22, 21, 16, 24, 15, 27, 23, 10]. This results into a tractable update load. The system is updated only when an object changes any of its moving parameters (e.g. speed, direction, etc) The alternative of storing the object s continuously changing location is practically infeasible since it would correspond to one update per ....
....future time t can be computed by o(t) o(0) o V t. A database that maintains the moving functions can compute and thus answer interesting queries about the locations of the moving objects in the future. Examples include range queries: nd which objects will be in area A, 10 minutes from now [10, 2, 17, 9, 22, 21, 20], nearest neighbor queries: nd the closest object(s) to a given location within the next 5 minutes [24] etc. The answer to such queries is based on the knowledge about the object movements at the time the query is issued [25, 26] In this paper we present a framework for answering ....
P. K. Agarwal, L. Arge, and J. Erickson. Indexing moving points. In Proc. of the 19th ACM Symp. on Principles of Database Systems (PODS), pages 175-186, 2000.
....of our techniques are (i) high accuracy (1 2 orders of magnitude lower error than previous techniques) ii) ability to handle all query types, and (iii) efficient handling of updates. 1. Introduction Spatio temporal database management systems (STDBMS) have received considerable attention [AAE00, KGT99, PJT99, SJLL00, SJ02, TP01, TP02] in recent years due to the emergence of numerous applications (e.g. traffic supervision, flight control, weather forecast, etc) that require management of continuously moving objects. An important operation in these systems is to predict objects future location based on information at the ....
Agarwal, P.K., Arge, L., Erickson, J. Indexing Moving Points. PODS, 2000.
....A number of approaches for indexing of the current and predicted future positions of moving points involve partitioning of the space into which the objects are embedded. Tayeb et al. 14] use PMR Quadtrees [11] Kollios et al. 8] employ the so called dual data transformation, and Agarwal et al. [1] use the ideas of so called kinetic data structures [3] While addressing similar problems, the approaches explored in these papers are not closely related to our work. Since the technique proposed in this paper builds on the basic ideas of the TPR tree, we review briefly the TPR tree and related ....
P. K. Agarwal, L. Arge, and J. Erickson. Indexing Moving Points. Proc. of the PODS Conf., pp. 175--186, 2000.
....change (at time T) C= p i S: T p i =T , where T p i is the influence time of point p i . This paper presents the first study on the theoretical complexity of validity queries, aiming at solutions with good worst case performance. Our discussion is based on the popular memory disk hierarchy [ASV99, AAE00], where each I O access transfers a page of B (i.e. page size) units of information from the disk to the main memory, which contains at least B pages (a reasonable assumption in practice) The query cost is measured as the number of disk pages visited. Our objective is to achieve fast query ....
....answers such queries optimally (i.e. logarithmic query cost and linear space consumption) Earlier, non optimal structures for RS and 3 sided queries can be found in [IKO87, KRVV96, RS94, SR95] The first study on RS queries for moving objects [KGT99a] deals with only 1D data. Agarwal et al. [AAE00] present several interesting results in the 2D space following the kinetic approach [BGH97] In particular, they show that if queries arrive in chronological order, a RS can be answered with the same time complexity as the static case (i.e. optimally) using the kinetic external range tree. They ....
[Article contains additional citation context not shown here]
Agarwal, P., Arge, L., Erickson, J. Indexing Moving Points. ACM PODS, 2000.
....with each query. Thus it is typically going to incur almost three orders of magnitude more comparisons than the others An earlier experiment to measure the total time required for Modify and Brute Force showed that their performance is very comparable despite the low 1 O cost of Brute Force [7]. Except for this special case, the I O cost is a good measure of performance. 6.2 Safe Region Optimizations We now study the relative performance of the safe region optimizations. For each scheme we plot the Reduction Rate: the fraction of moved objects that are within their safe region. These ....
P. K. Agarwal, L. Arge, and J. Erickson. Indexing moving points. In Proc. 2000.
....have different goals (i.e. retrieval of information about the past instead of the future) Kollios et al. KGT99] establish lower bounds for the cost of answering predictive window queries (using linear, or non linear space) and design several nearlyoptimal indexes for 1D objects. Agarwal et al. [AAE00] extend the solutions to two dimensions with the kinetic approach [BGH97] Although the resulting methods have good asymptotical performance, they are not applicable in practice due to the large hidden constants. From the practical perspective, Tayeb et al. TUW98] adapt the Quadtree [S90] for ....
Agarwal, P., Arge, L., Erickson, J. Indexing Moving Points. PODS, 2000.
....highly accurate estimation on both uniform and non uniform data. To appear in ACM TODS Keywords: Spatio Temporal Databases, Selectivity Estimation, Probabilistic Analysis, Histograms 1. INTRODUCTION Spatio temporal database management systems (STDBMS) have received considerable attention [KGT99, AAE00, PJT00, SJLL00, HKTG02, SJ02, TP02] in recent years due to the emergence of numerous applications (e.g. traffic supervision, flight control, weather forecast, etc) that require management of continuously moving objects. An important operation in these systems is to predict objects future location based on information at the ....
Agarwal, P., Arge, L., Erickson, J. Indexing Moving Points. ACM PODS, 2000.
....map moving objects and their velocities into points and store the points in a kD tree. Pfoser et al. 26] 25] index the past trajectories of moving objects that are presented as connected line segments. The problem of answering a range query for a collection of moving objects is addressed in [3] through the use of indexing schemes using external range trees. Wolfson et al. 36] 38] consider the management of collections of moving points in the plane by describing the current and expected positions of each point in the future. They address how often to update the locations of the points ....
P.K. Agarwal, L. Arge, and J. Erickson, "Indexing Moving Points," Proc. 2000.
....STDB, 64] adapts the Quadtree [53] a spatial index) for indexing the movements of 1D objects, while the time parameterized R tree [51] TPR tree) and its improved versions [50, 61] support objects of arbitrary dimensionality. Finally, indexing moving objects has also been studied in theory [44, 34, 56, 49], which develop numerous interesting structures with provable worst case performance bounds. These bounds, however, usually involve large hidden constants, rendering these theoretical solutions to be outperformed by the practical solutions introduced earlier. 5 Indexing XML by Tree ....
P. Agarwal, L. Arge, and J. Erickson. Indexing moving points. PODS, 2000.
....sequences of multidimensional points. They extend the ideas presented by Faloutsos et al. in [12] and the similarity model is based on the Euclidean distance. Recently, there has been some work on indexing moving objects to answer spatial proximity queries (range and nearest neighbor queries) [19, 1, 27]. Also in [23] Pfoser et al. present index methods to answer topological and navigational queries in a database that stores trajectories of moving objects. These works do not consider a global similarity model between trajectories but they concentrate on finding objects that are close to query ....
P. K. Agarwal, L. Arge, and J. Erickson. Indexing moving points. In Proc. of the 19th ACM Symp. on Principles of Database Systems (PODS), pages 175--186, 2000.
....and in absence of noise, which is definitely not the case for moving objects. This paper describes di#erent approaches to aggregate similar trajectories. 1. INTRODUCTION Moving object representation and computing has received a fair share of attention over recent years in the database community [27, 14, 29, 22, 1, 6, 26]. This is understandable as positioning technology is rapidly making its way into the consumer market, not only through the already ubiquitous cell phone but soon also through small, on board positioning Permission to make digital or hard copies of all or part of this work for personal or ....
P. K. Agarwal, L. Arge, and J. Erickson. Indexing moving points. In Symposium on Principles of Database Systems, pp. 175--186, 2000.
....into two categories: queries that ask questions about the future positions of moving points, and queries that ask questions about the historical positions of moving objects. The former class of queries can be answered by storing current position, speed and the direction of the moving objects [1, 14, 24, 25]. For the second class of queries, Pfoser et al. 21] further classify historical queries into two different sub classes: coordinate based queries and trajectorybased queries. Coordinate based queries include (a) timeinterval, which select all objects within a given area and give time period, b) ....
AGARWAL,P.K.,ARGE,L.,AND ERICKSON,J. Indexing Moving Points. In Proceedings of the Nineteenth ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems (Dallas, Texas, USA, May 2000), pp. 175--186.
....a certain point in space) etc. A major difference from continuous queries in the context of traditional databases, is that in case of spario temporal databases, the object s dynamic behavior does not necessarily require updates, but can be stored as a function of time using appropriate indexes [BJSS98, TUW98, KGT99, AAE00, SJLL00]. Furthermore even if the objects are static, the results may change due to the dynamic nature of the query itself (i.e. moving query window) which can be also represented as a function of time. Thus, a spario temporal continuous query can be evaluated instantly (i.e. at the current time) using ....
Agarwal, P.K., Arge, L., Erickson, J. Indexing Moving Points. ACMSIGMOD, 2000.
....culminating with the result of Matousek [Mat92] who obtained O(n 1 1 #d 2# polylog(n) t) query cost, still with linear space. These techniques were adapted to external memory by the works of Agarwal et al. AAE 98] Kollios, Gunopoulos and Tsotras [KGT99] and Agarwal, Arge and Erickson [AAE00] Another series of techniques began with the work of Chazelle, Guibas and Lee [CGL85] who introduced to the problem the concept of arrangements. For the planar case, their technique achieves optimal time O(log n t) with linear space. However, generalizing the approach to higher dimensions, ....
.... in the P range tree [SR95] by Arge and Vitter in the External Interval Tree [AV96] and by Vengro# and Vitter in their 3 dimensional index structures [VV96a] Since our work, it has been employed by Agarwal et al. AAE 98] to indexing for half space queries, and moving points on the plane [AAE00] The main merit of bootstrapping as a general approach, is that it does not (potentially) su#er from the weaknesses of the Path Caching technique of Ramaswamy and Subramanian, discussed in Sec. 6.2.2. The main drawback is that it assumes a solution to the underlying indexability problem. Such ....
P.K. Agarwal, L. Arge, and J. Erickson. Indexing moving points. In 2000.
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P. K. Agarwal, L. Arge, and J. Erickson. Indexing moving points. In Proc. 19th ACM Sympos. Principles Database Syst., pages 175-186, 2000.
.... of existing database systems to represent moving object databases (MOD) and on indexing moving objects; see, e.g. 14, 22, 23] The known data structures for answering range queries on moving points either do not guarantee a worst case bound on the query time [26, 25, 19] or are too complicated [1, 15]. In this paper we develop kinetic data structures for kd trees, a widely used data structure for answering various proximity queries in practice [10] which can e#ciently answer range queries on moving points. The kinetic data structure framework, originally proposed by Basch et al. 5] has led ....
....It is well known that a kd tree can answer a two dimensional orthogonal range query in O( # n k) time, where k is the number of points reported. Variants of kd trees that support insertions and deletions are studied in [18, 9] No kinetic data structures are known for kd trees. Agarwal et al. [1] were the first to develop kinetic data structures for answering range searching queries on moving points. They developed a kinetic data structure that answers a two dimensional range query in O(log n k) time using O(n log n (log log n) space, where k is the output size. The amortized cost of a ....
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P. K. Agarwal, L. Arge, and J. Erickson. Indexing moving points. In Proc. Annu. ACM Sympos. Principles Database Syst., 2000. 175--186.
....amortized cost of O(log n) expected I Os each. 2. 3 Simplified partition trees for random points We can significantly simplify the partition tree data structure if the points in are distributed uniformly and independently in some rectangular domain, which we can take to be the unit square C = [0, 1] 2 with no loss of generality. For simplicity, assume that B = 4 s for some integer s 0. We call our simplified data structure a grid tree, which is a variant of the so called hierarchical grid file [31] At a high level, the grid tree 6 is a B ary tree of depth log s n. Each node v in 6 is ....
....Overmars, similarly to partition trees above. The expected amortized cost to insert or delete a random point is only O(log B n) I Os, in part because we can directly compute which cell of a grid contains a given point at each node. Theorem 2.5. Given a set S of N uniformly distributed points in [0, 1] 2, we can preprocess S into an index of size O(n) blocks so that the points inside a query strip can be found in O( v q k ) 1 Os Indexin Movin Points 9 with probability at least 1 1 N. The index can be constructed in O(n log B n) 1 Os, and random points can be inserted or deleted at an ....
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P. K. Agarwal, L. Arge, J. Erickson, Indexing moving points, Proc. 19th Annu. ACM Sympos. Principles Database $yst., 175-186, 2000.
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P.K. Agarwal, L. Arge, J. Erickson: "Indexing Moving Points", Proceedings 19th ACM Symposium on Principles of Database Systems (PODS'2000), pp.175-186, Madison, WI, 2000.
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P.K. Argarwal, L. Arge, and J. Erickson, "Indexing Moving Points," Proc. ACM Symp. Principles of Database Systems, pp. 175186, 2000.
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P. K. Argarwal, L. Arge, and J. Erickson. Indexing moving points. In Proc. of ACM PODS'00, pages 175--186, 2000.
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P. K Agarwal, L. Arge, and J. Erickson. Indexing moving points. In Symposium on Principles of Database Systems pp. 175--186, 2000.
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P. Agarwal, L. Arge, and J. Erickson. Indexing moving points. In Symposium on Principles of Database Systems, pages 175--186, 2000.
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Pankaj K. Agarwal, Lars Arge, and Jeff Erickson. Indexing moving points. In ACM PODS, 2000.
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P. K. Agarwal, L. Arge, and J. Erickson. Indexing moving points. In PODS, 2000.
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P. K. Agarwal, L. Arge, and J. Erickson. Indexing Moving Points. Proc. of the PODS Conf., pp. 175--186 (2000).
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P. K. Agarwal, L. Arge, and J. Erickson. Indexing Moving Points. Proc. of the PODS Conf., pp. 175--186 (2000).
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P. K. Agarwal, L. Arge, and J. Erickson. Indexing Moving Points. Proc. of PODS, pp. 175--186, 2000.
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P. K. Agarwal, L. Arge, and J. Erickson. Indexing moving points. In Proc. of the ACM Symposium on Principles of Database Systems (PODS), 2000, 175-- 186.
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P. K. Agarwal, L. Arge, and J. Erickson. Indexing Moving Points. Proc. of the PODS Conf., pp. 175--186 (2000).
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P. K. Agarwal, L. Arge, and J. Erickson. Indexing Moving Points. Proc. of the PODS Conf., pp. 175--186, 2000.
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Pankaj K. Agarwal, Lars Arge, and Jeff Erickson. Indexing moving points. In Proceedings of the ACM Symposium on Principles of Database Systems (PODS), pages 175--186, 2000. 7
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P. K. Agarwal, L. Arge, and J. Erickson. Indexing Moving Points. Proc. of the PODS Conf., pp. 175--186 (2000).
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Agarwal PK,Arge L, Erickson J (2000) Indexing moving points. Proc. 2000 PODS Conference, pp. 175--186
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Pankaj K. Agarwal, Lars Arge, and Je# Erickson. Indexing moving points. In Proceedings of the ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems, Dallas, Texas, May 2000.
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P. Agarwal, L. Arge, and J. Erickson. Indexing moving points. In Proc. of the 19th Conf. on Principles of Database Systems (PODS), 2000.
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P. K. Agarwal, L. Arge, and J. Erickson. Indexing Moving Points. In Proceedings of the 19th ACM Symp. on Principles of Database Systems, pages 175--186, 2000.
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P. K. Agarwal, L. Arge, and J. Erickson. Indexing moving points. In Symposium on Principles of Database Systems, pages 175--186, 2000.
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P. K. Agarwal, L. Arge, and J. Erickson. Indexing moving points. In Proc. 19th ACM Sympos. Principles Database Syst., pages 175-186, 2000.
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Pankaj K. Agarwal, Lars Arge, and Jeff Erickson. Indexing moving points. In Proceedings of the Nineteenth ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems, May 1517 2000.
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P. K. Argarwal, L. Arge, and J. Erickson. Indexing moving points. In Proc. of ACM PODS'00, pages 175--186, 2000.
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P.K. Agarwal, L. Arge and J. Erickson. Indexing Moving Points In Proc. 19th ACM PODS Symposium on Principles of Database Systems, May 2000.
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Agarwal, P.K., Arge, L. and Erickson, J., Indexing Moving Points. In PODS, 2000, 175-186.
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P. K. Agarwal, I. Arge, and J.Erickson. Indexing moving points. Proc. 2000.
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P. K. Agarwal, L. Arge, and J. Erickson. Indexing Moving Points. In Proc. of the ACM Symp. on Principles of Database Systems, PODS, pages 175--186, May 2000.
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P.K. Agarwal, L. Arge, J. Erickson: "Indexing Moving Points", Proceedings 19th ACM Symposium on Principles of Database Systems (PODS'2000), pp.175-186, Madison, WI, 2000.
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P. K. Agarwal, I. Arge, and J. Erickson. Indexing moving points. Proc. 2000.
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P. K. Agarwal, L. Arge, and J. Erickson. Indexing moving points. In Proc. 2000.
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P. K. Agarwal, L. Arge, and J. Erickson. Indexing moving points. In Proc. of the 19th ACM Symp. on Principles of Database Systems (PODS), pages 175--186, 2000.
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Agarwal, P.K., Arge, L., Erickson, J. Indexing Moving Points. ACM SIGMOD, 2000.
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