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62
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 191 (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
Continuous Nearest Neighbor Search
, 2002
"... A continuous nearest neighbor query retrieves the nearest neighbor (NN) of every point on a line segment (e.g., "find all my nearest gas stations during my route from point s to point e"). The result contains a set of <point, interval> tuples, such that point is the NN of all po ..."
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Cited by 159 (10 self)
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A continuous nearest neighbor query retrieves the nearest neighbor (NN) of every point on a line segment (e.g., "find all my nearest gas stations during my route from point s to point e"). The result contains a set of <point, interval> tuples, such that point is the NN of all points in the corresponding interval. Existing methods for continuous nearest neighbor search are based on the repetitive application of simple NN algorithms, which incurs significant overhead. In this paper we propose techniques that solve the problem by performing a single query for the whole input segment. As a result the cost, depending on the query and dataset characteristics, may drop by orders of magnitude.
Monitoring kNearest Neighbor Queries Over Moving Objects
"... Many locationbased applications require constant monitoring of knearest neighbor (kNN) queries over moving objects within a geographic area. Existing approaches to this problem have focused on predictive queries, and relied on the assumption that the trajectories of the objects are fully predicta ..."
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Cited by 127 (0 self)
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Many locationbased applications require constant monitoring of knearest neighbor (kNN) queries over moving objects within a geographic area. Existing approaches to this problem have focused on predictive queries, and relied on the assumption that the trajectories of the objects are fully predictable at query processing time. We relax this
Nearest Neighbor and Reverse Nearest Neighbor Queries for Moving Objects
, 2001
"... With the proliferation of wireless communications and the rapid advances in technologies for tracking the positions of continuously moving objects, algorithms for efficiently answering queries about large numbers of moving objects increasingly are needed. One such query is the reverse nearest neighb ..."
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Cited by 120 (9 self)
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With the proliferation of wireless communications and the rapid advances in technologies for tracking the positions of continuously moving objects, algorithms for efficiently answering queries about large numbers of moving objects increasingly are needed. One such query is the reverse nearest neighbor (RNN) query that returns the objects that have a query object as their closest object. While algorithms have been proposed that compute RNN queries for nonmoving objects, there have been no proposals for answering RNN queries for continuously moving objects. Another such query is the nearest neighbor (NN) query, which has been studied extensively and in many contexts. Like the RNN query, the NN query has not been explored for moving query and data points. This paper proposes an algorithm for answering RNN queries for continuously moving points in the plane. As a part of the solution to this problem and as a separate contribution, an algorithm for answering NN queries for continuously moving points is also proposed. The results of performance experiments are reported.
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.
Aggregate Nearest Neighbor Queries in Spatial Databases
 TODS
, 2005
"... Given two spatial datasets P (e.g., facilities) and Q (queries), an aggregate nearest neighbor (ANN) query retrieves the point(s) of P with the smallest aggregate distance(s) to points in Q. Assuming, for example, n users at locations q1,... qn,anANN query outputs the facility p ∈ P that minimizes t ..."
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Cited by 59 (6 self)
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Given two spatial datasets P (e.g., facilities) and Q (queries), an aggregate nearest neighbor (ANN) query retrieves the point(s) of P with the smallest aggregate distance(s) to points in Q. Assuming, for example, n users at locations q1,... qn,anANN query outputs the facility p ∈ P that minimizes the sum of distances pqi  for 1 ≤ i ≤ n that the users have to travel in order to meet there. Similarly, another ANN query may report the point p ∈ P that minimizes the maximum distance that any user has to travel, or the minimum distance from some user to his/her closest facility. If Q fits in memory and P is indexed by an Rtree, we develop algorithms for aggregate nearest neighbors that capture several versions of the problem, including weighted queries and incremental reporting of results. Then, we analyze their performance and propose cost models for query optimization. Finally, we extend our techniques for diskresident queries and approximate ANN retrieval. The efficiency of the algorithms and the accuracy of the cost models are evaluated through extensive experiments with real and synthetic datasets.
Semantic Caching in LocationDependent Query Processing
 In SSTD
, 2001
"... A method is presented in this paper for answering locationdependent queries in a mobile computing environment. We investigate a common scenario where data objects (e.g., restaurants and gas stations) are stationary while clients that issue queries about the data objects are mobile. Our proposed ..."
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Cited by 39 (4 self)
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A method is presented in this paper for answering locationdependent queries in a mobile computing environment. We investigate a common scenario where data objects (e.g., restaurants and gas stations) are stationary while clients that issue queries about the data objects are mobile. Our proposed technique constructs a Voronoi Diagram (VD) on the data objects to serve as an index for them. A VD defines, for each data object d, the region within which d is the nearest point to any mobile client within that region. As such, the VD can be used to answer nearestneighbor queries directly. Furthermore, the area within which the answer is valid can be computed. Based on the VD, we develop a semantic caching scheme that records a cached item as well as its valid range. A simulation is conducted to study the performance of the proposed semantic cache in comparison with the traditional cache and the baseline case where no cache is used. We show that the semantic cache has a much better performance than the other two methods. Keywords: mobile computing, locationdependent query, Voronoi Diagrams.
OnLine Discovery of Dense Areas in SpatioTemporal Databases
 In Proc. SSTD
, 2003
"... Abstract — Moving object databases have received considerable attention recently. Previous work has concentrated mainly on modeling and indexing problems, as well as query selectivity estimation. Here we introduce a novel problem, that of addressing densitybased queries in the spatiotemporal domai ..."
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Cited by 32 (1 self)
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Abstract — Moving object databases have received considerable attention recently. Previous work has concentrated mainly on modeling and indexing problems, as well as query selectivity estimation. Here we introduce a novel problem, that of addressing densitybased queries in the spatiotemporal domain. For example: “Find all regions that will contain more than 500 objects, ten minutes from now”. The user may also be interested in finding the time period (interval) that the query answer remains valid. We formally define a new class of densitybased queries and give approximate, online techniques that answer them efficiently. Typically the threshold above which a region is considered to be dense is part of the query. The difficulty of the problem lies in the fact that the spatial and temporal predicates are not specified by the query. The techniques we introduce find all candidate dense regions at any time in the future. To make them more scalable we subdivide the spatial universe using a grid and limit queries within a prespecified time horizon. Finally, we validate our approaches with a thorough experimental evaluation. I.
Adaptive stream filters for entitybased queries with nonvalue tolerance
 in VLDB
, 2005
"... We study the problem of applying adaptive filters for approximate query processing in a distributed stream environment. We propose filter bound assignment protocols with the objective of reducing communication cost. Most previous works focus on valuebased queries (e.g., average) with numerical erro ..."
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Cited by 31 (5 self)
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We study the problem of applying adaptive filters for approximate query processing in a distributed stream environment. We propose filter bound assignment protocols with the objective of reducing communication cost. Most previous works focus on valuebased queries (e.g., average) with numerical error tolerance. In this paper, we cover entitybased queries (e.g., a nearest neighbor query returns object names rather than a single value). In particular, we study nonvaluebased tolerance (e.g., the answer to the nearestneighbor query should rank third or above). We investigate different nonvaluebased error tolerance definitions and discuss how they are applied to two classes of entitybased queries: nonrankbased and rankbased queries. Extensive experiments show that our protocols achieve significant savings in both communication overhead and server computation. 1