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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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\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.
Dynamic Data Structures for Fat Objects and Their Applications
, 1999
"... We present several efficient dynamic data structures for pointenclosure queries, involving convex fat objects in R2 or R3. Our planar structures are actually fitted for a more general class of objects (fi; ffi)covered objects which are not necessarily convex, see definition below. These stru ..."
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We present several efficient dynamic data structures for pointenclosure queries, involving convex fat objects in R2 or R3. Our planar structures are actually fitted for a more general class of objects (fi; ffi)covered objects which are not necessarily convex, see definition below. These structures are more efficient than alternative known structures, because they exploit the fatness of the objects. We then apply these structures to obtain efficient solutions to two problems (i) Finding a perfect containment matching between a set of points and a set of convex fat objects. (ii) Finding a piercing set for a collection of convex fat objects, whose size is optimal up to some constant factor.
Approximating Spanning Trees with Low Crossing Number
, 2009
"... We present a linear programming based algorithm for computing a spanning tree T of a set P of n points in IR d, such that its crossing number is O(min(t log n, n 1−1/d)), where t the minimum crossing number of any spanning tree of P. This is the first guaranteed approximation algorithm for this prob ..."
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Cited by 2 (0 self)
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We present a linear programming based algorithm for computing a spanning tree T of a set P of n points in IR d, such that its crossing number is O(min(t log n, n 1−1/d)), where t the minimum crossing number of any spanning tree of P. This is the first guaranteed approximation algorithm for this problem. We provide a similar approximation algorithm for the more general settings of building a spanning tree for a set system with bounded VC dimension. Our approach is an alternative to the reweighting technique previously used in computing such spanning trees. 1
OutputSensitive Algorithms for Uniform Partitions of Points
 PROCEEDINGS OF THE 10TH INTERNATIONAL SYMPOSIUM ON ALGORITHMS AND COMPUTATION, ISAAC, VOLUME 1741 OF LECTURE NOTES IN COMPUTER SCIENCE
, 1999
"... We consider the following one and twodimensional bucketing problems: Given a set S of n points in R 1 or R 2 and a positive integer b, distribute the points of S into b equalsize buckets so that the maximum number of points in a bucket is minimized. Suppose at most (n=b)+ \Delta points lies i ..."
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Cited by 2 (1 self)
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We consider the following one and twodimensional bucketing problems: Given a set S of n points in R 1 or R 2 and a positive integer b, distribute the points of S into b equalsize buckets so that the maximum number of points in a bucket is minimized. Suppose at most (n=b)+ \Delta points lies in each bucket in an optimal solution. We present algorithms whose time complexities depend on b and \Delta. No prior knowledge of \Delta is necessary for our algorithms. For the onedimensional problem, we give a deterministic algorithm that achieves a running time of O(b 4 (\Delta 2 + log n) + n). For the twodimensional problem, we present a MonteCarlo algorithm that runs in subquadratic time for certain values of b and \Delta. The previous algorithms, by Asano and Tokuyama [1], searched the entire parameterized space and required\Omega\Gamma n 2 ) time in the worst case even for constant values of b and \Delta. We also present a subquadratic algorithm for the special case of the ...
The VLDB Journal (2004) / Digital Object Identifier (DOI) 10.1007/s007780040139z Indexing mobile objects using dual transformations
"... Abstract. With the recent advances in wireless networks, embedded ..."
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Exact and approximate Geometric Pattern Matching for point sets in the plane under similarity transformations
 CCCG
, 2007
"... ..."
An Indexing Method for Answering Queries on Moving Objects
"... + K=B) I/O's using O(N=B) space, where B is the block size, and K is the number of reported points. Our approach is novel in that, while it provides a theoretical upper bound on the average query time, it avoids the use of complicated data structures, making it an effective candidate for practi ..."
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+ K=B) I/O's using O(N=B) space, where B is the block size, and K is the number of reported points. Our approach is novel in that, while it provides a theoretical upper bound on the average query time, it avoids the use of complicated data structures, making it an effective candidate for practical applications. The proposed index is also dynamic in the sense that it allows object insertion and deletion in an amortized update cost of logB(N) I/O's. Experimental results are presented to show the superiority of the proposed index over other methods based on Rtrees. Keywords: B+trees, indexing, mobile objects, mobile database management, query processing. 1 Introduction The last decade has witnessed a rapid and continuous growth in positioning systems and wireless communication technologies. In particular, the vast explosion of technological progress in portable laptops, smaller palmtop computers, mobile phones, and smart cars had made it possible to establish a whole new paradigm of wireless computing [3], and its associated implications on a wide range of fields.
INDEXING OF MOVING OBJECTS
"... With the recent advances in wireless networks, embedded systems, and GPS technology, databases that manage the location of moving objects have received increased interest. In particular, we propose methods to index moving objects in order to efficiently answer range queries about their current and f ..."
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With the recent advances in wireless networks, embedded systems, and GPS technology, databases that manage the location of moving objects have received increased interest. In particular, we propose methods to index moving objects in order to efficiently answer range queries about their current and future positions. We address the problem in external memory and present dynamic solutions, both for the onedimensional and the twodimensional cases. Our approach transforms the problem into a dual space that is easier to index. 1.