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52
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 223 (16 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...
Efficient Indexing Methods for Probabilistic Threshold Queries over Uncertain Data
 Proc. 30th Int’l Conf. Very Large Data Bases (VLDB
, 2004
"... It is infeasible for a sensor database to contain the exact value of each sensor at all points in time. This uncertainty is inherent in these systems due to measurement and sampling errors, and resource limitations. In order to avoid drawing erroneous conclusions based upon stale data, the use of un ..."
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Cited by 125 (22 self)
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It is infeasible for a sensor database to contain the exact value of each sensor at all points in time. This uncertainty is inherent in these systems due to measurement and sampling errors, and resource limitations. In order to avoid drawing erroneous conclusions based upon stale data, the use of uncertainty intervals that model each data item as a range and associated probability density function (pdf) rather than a single value has recently been proposed. Querying these uncertain data introduces imprecision into answers, in the form of probability values that specify the likeliness the answer satisfies the query. These queries are more expensive to evaluate than their traditional counterparts but are guaranteed to be correct and more informative due to the probabilities accompanying the answers. Although the answer probabilities are useful, for many applications, it is only necessary to know whether the probability exceeds a given threshold – we term these Probabilistic Threshold Queries (PTQ). In this paper we address the efficient computation of these types of queries. In particular, we develop two index structures and associated algorithms to efficiently answer PTQs. The first index scheme is based on the idea of augmenting uncertainty information to an Rtree. We establish the difficulty
Arrangements and Their Applications
 Handbook of Computational Geometry
, 1998
"... The arrangement of a finite collection of geometric objects is the decomposition of the space into connected cells induced by them. We survey combinatorial and algorithmic properties of arrangements of arcs in the plane and of surface patches in higher dimensions. We present many applications of arr ..."
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Cited by 89 (20 self)
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The arrangement of a finite collection of geometric objects is the decomposition of the space into connected cells induced by them. We survey combinatorial and algorithmic properties of arrangements of arcs in the plane and of surface patches in higher dimensions. We present many applications of arrangements to problems in motion planning, visualization, range searching, molecular modeling, and geometric optimization. Some results involving planar arrangements of arcs have been presented in a companion chapter in this book, and are extended in this chapter to higher dimensions. Work by P.A. was supported by Army Research Office MURI grant DAAH049610013, by a Sloan fellowship, by an NYI award, and by a grant from the U.S.Israeli Binational Science Foundation. Work by M.S. was supported by NSF Grants CCR9122103 and CCR9311127, by a MaxPlanck Research Award, and by grants from the U.S.Israeli Binational Science Foundation, the Israel Science Fund administered by the Israeli Ac...
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.
Efficient Searching with Linear Constraints (Extended Abstract)
"... We show how to preprocess a set S of points in R d to get an external memory data structure that efficiently supports linearconstraint queries. Each query is in the form of a linear constraint a \Delta x b; the data structure must report all the points of S that satisfy the query. Our goal i ..."
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Cited by 57 (16 self)
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We show how to preprocess a set S of points in R d to get an external memory data structure that efficiently supports linearconstraint queries. Each query is in the form of a linear constraint a \Delta x b; the data structure must report all the points of S that satisfy the query. Our goal is to minimize the number of disk blocks required to store the data structure and the number of disk accesses (I/Os) required to answer a query. For d = 2, we present the first nearlinear size data structures that can answer linearconstraint queries using an optimal number of I/Os. We also present a linearsize data structure that can answer queries efficiently in the worst case. We combine these two approaches to obtain tradeoffs between space and query time. Finally, we show that some of our techniques extend to higher dimensions d.
Random Sampling, Halfspace Range Reporting, and Construction of (≤k)Levels in Three Dimensions
 SIAM J. COMPUT
, 1999
"... Given n points in three dimensions, we show how to answer halfspace range reporting queries in O(logn+k) expected time for an output size k. Our data structure can be preprocessed in optimal O(n log n) expected time. We apply this result to obtain the first optimal randomized algorithm for the co ..."
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Cited by 38 (8 self)
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Given n points in three dimensions, we show how to answer halfspace range reporting queries in O(logn+k) expected time for an output size k. Our data structure can be preprocessed in optimal O(n log n) expected time. We apply this result to obtain the first optimal randomized algorithm for the construction of the ( k)level in an arrangement of n planes in three dimensions. The algorithm runs in O(n log n+nk²) expected time. Our techniques are based on random sampling. Applications in two dimensions include an improved data structure for "k nearest neighbors" queries, and an algorithm that constructs the orderk Voronoi diagram in O(n log n + nk log k) expected time.
Efficient Aggregation over Objects with Extent (Extended Abstract)
 TechReport UCR CS 01 01, CS Dept
, 2002
"... We examine the problem of efficiently computing sum/count/avg aggregates over... ..."
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Cited by 37 (8 self)
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We examine the problem of efficiently computing sum/count/avg aggregates over...
Using the Triangle Inequality to Reduce the Number of Comparisons Required for SimilarityBased Retrieval
 Proc. of SPIE/IS&T Conf. on Storage and Retrieval for Image and Video Databases IV
, 1996
"... Dissimilarity measures, the basis of similaritybased retrieval, can be viewed as a distance and a similaritybased search as a nearest neighbor search. Though there has been extensive research on data structures and search methods to support nearestneighbor searching, these indexing and dimensionr ..."
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Cited by 32 (1 self)
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Dissimilarity measures, the basis of similaritybased retrieval, can be viewed as a distance and a similaritybased search as a nearest neighbor search. Though there has been extensive research on data structures and search methods to support nearestneighbor searching, these indexing and dimensionreduction methods are generally not applicable to noncoordinate data and nonEuclidean distance measures. In this paper we reexamine and extend previous work of other researchers on best match searching based on the triangle inequality. These methods can be used to organize both noncoordinate data and nonEuclidean metric similarity measures. The effectiveness of the indexes depends on the actual dimensionality of the feature set, data, and similarity metric used. We show that these methods provide significant performance improvements and may be of practical value in realworld databases. Keywords: image database indexing, similaritybased retrieval, best match searching, triangle inequali...
Range counting over multidimensional data streams
 Discrete & Computational Geometry
, 2004
"... \Lambda \Lambda Abstract We consider the problem of approximate range counting over streams of ddimensional points. In the data stream model, the algorithm makes a single scan of the data, which is presented in an arbitrary order, and computes a compact summary (called a sketch). The sketch, whose ..."
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Cited by 31 (0 self)
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\Lambda \Lambda Abstract We consider the problem of approximate range counting over streams of ddimensional points. In the data stream model, the algorithm makes a single scan of the data, which is presented in an arbitrary order, and computes a compact summary (called a sketch). The sketch, whose size depends on the approximation parameter &quot;, can be used to count the number of points inside a query range within additive error &quot;n, where n is the size of the stream. We present several results, deterministic and randomized, for both rectangle and halfplane ranges. 1 Introduction Data streams have emerged as an important paradigm for processing data that arrives and needs to be processed continuously. For instance, telecom service providers routinely monitor packet flows through their networks to infer usage patterns and signs of attack, or to optimize their routing tables. Financial markets, banks, web servers, and news organizations also generate rapid and continuous data streams.