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Approximating the Radii of Point Sets
, 2005
"... We consider the problem of computing the outerradii of point sets. Inthis problem, we are given integers n, d, k where k < = d, and a set P of n points in Rd. The goal is to compute the outer kradius of P, denoted by Rk(P), which is the minimum, over all (d k)dimensional flats F, ofmax p2P d( ..."
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Cited by 11 (1 self)
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We consider the problem of computing the outerradii of point sets. Inthis problem, we are given integers n, d, k where k < = d, and a set P of n points in Rd. The goal is to compute the outer kradius of P, denoted by Rk(P), which is the minimum, over all (d k)dimensional flats F, ofmax p2P d
An Improved Algorithm for Approximating the Radii of Point Sets
 In RANDOMAPPROX
, 2003
"... We consider the problem of computing the outerradii of point sets. In this problem, we are given integers n; d; k where k d, and a set P of n points in R ats F , of max p2P d(p; F ), where d(p; F ) is the Euclidean distance between the point p and at F . Computing the radii of point sets is a ..."
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Cited by 8 (2 self)
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We consider the problem of computing the outerradii of point sets. In this problem, we are given integers n; d; k where k d, and a set P of n points in R ats F , of max p2P d(p; F ), where d(p; F ) is the Euclidean distance between the point p and at F . Computing the radii of point sets
Approximating the radii of point sets in high dimensions
 In Proc. 43th Annu. IEEE Sympos. Found. Comput. Sci
, 2002
"... Abstract Let P be a set of n points in Rd. For any 1 < = k < = d, the outer kradius of P, denotedby Rk(P), is the minimum, over all (d k)dimensional flats F, of maxp2P d(p, F),where d(p, F) is the Euclidean distance between the point p and flat F. We considerthe scenario when the dimension ..."
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Cited by 5 (2 self)
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d is not fixed and can be as large as n. Computing thevarious radii of point sets is a fundamental problem in computational convexity with many applications (See [18]).The main result of this paper is a randomized polynomial time algorithm that approximates Rk(P) to within a factor of O(plog n * log
A Threshold of ln n for Approximating Set Cover
 JOURNAL OF THE ACM
, 1998
"... Given a collection F of subsets of S = f1; : : : ; ng, set cover is the problem of selecting as few as possible subsets from F such that their union covers S, and max kcover is the problem of selecting k subsets from F such that their union has maximum cardinality. Both these problems are NPhar ..."
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Cited by 778 (5 self)
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hard. We prove that (1 \Gamma o(1)) ln n is a threshold below which set cover cannot be approximated efficiently, unless NP has slightly superpolynomial time algorithms. This closes the gap (up to low order terms) between the ratio of approximation achievable by the greedy algorithm (which is (1 \Gamma
Approximate Signal Processing
, 1997
"... It is increasingly important to structure signal processing algorithms and systems to allow for trading off between the accuracy of results and the utilization of resources in their implementation. In any particular context, there are typically a variety of heuristic approaches to managing these tra ..."
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Cited by 516 (2 self)
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these tradeoffs. One of the objectives of this paper is to suggest that there is the potential for developing a more formal approach, including utilizing current research in Computer Science on Approximate Processing and one of its central concepts, Incremental Refinement. Toward this end, we first summarize a
Surface reconstruction from unorganized points
 COMPUTER GRAPHICS (SIGGRAPH ’92 PROCEEDINGS)
, 1992
"... We describe and demonstrate an algorithm that takes as input an unorganized set of points fx1�:::�xng IR 3 on or near an unknown manifold M, and produces as output a simplicial surface that approximates M. Neither the topology, the presence of boundaries, nor the geometry of M are assumed to be know ..."
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Cited by 811 (8 self)
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We describe and demonstrate an algorithm that takes as input an unorganized set of points fx1�:::�xng IR 3 on or near an unknown manifold M, and produces as output a simplicial surface that approximates M. Neither the topology, the presence of boundaries, nor the geometry of M are assumed
Approximate Nearest Neighbors: Towards Removing the Curse of Dimensionality
, 1998
"... The nearest neighbor problem is the following: Given a set of n points P = fp 1 ; : : : ; png in some metric space X, preprocess P so as to efficiently answer queries which require finding the point in P closest to a query point q 2 X. We focus on the particularly interesting case of the ddimens ..."
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Cited by 1017 (40 self)
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The nearest neighbor problem is the following: Given a set of n points P = fp 1 ; : : : ; png in some metric space X, preprocess P so as to efficiently answer queries which require finding the point in P closest to a query point q 2 X. We focus on the particularly interesting case of the d
The space complexity of approximating the frequency moments
 JOURNAL OF COMPUTER AND SYSTEM SCIENCES
, 1996
"... The frequency moments of a sequence containing mi elements of type i, for 1 ≤ i ≤ n, are the numbers Fk = �n i=1 mki. We consider the space complexity of randomized algorithms that approximate the numbers Fk, when the elements of the sequence are given one by one and cannot be stored. Surprisingly, ..."
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Cited by 855 (12 self)
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The frequency moments of a sequence containing mi elements of type i, for 1 ≤ i ≤ n, are the numbers Fk = �n i=1 mki. We consider the space complexity of randomized algorithms that approximate the numbers Fk, when the elements of the sequence are given one by one and cannot be stored. Surprisingly
Spacetime Interest Points
 IN ICCV
, 2003
"... Local image features or interest points provide compact and abstract representations of patterns in an image. In this paper, we propose to extend the notion of spatial interest points into the spatiotemporal domain and show how the resulting features often reflect interesting events that can be use ..."
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Cited by 791 (22 self)
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Local image features or interest points provide compact and abstract representations of patterns in an image. In this paper, we propose to extend the notion of spatial interest points into the spatiotemporal domain and show how the resulting features often reflect interesting events that can
Results 1  10
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