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CLOSESTPOINT PROBLEMS
"... A number of seemingly unrelated problems involving the proximity of N points in the plane are studied, such as finding a Euclidean minimum spanning tree, the smallest circle enclosing the set, k nearest and farthest neighbors, the two closest points, and a proper straightline triangulation. For mos ..."
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A number of seemingly unrelated problems involving the proximity of N points in the plane are studied, such as finding a Euclidean minimum spanning tree, the smallest circle enclosing the set, k nearest and farthest neighbors, the two closest points, and a proper straightline triangulation
ClosestPoint Problems in Computational Geometry
, 1997
"... This is the preliminary version of a chapter that will appear in the Handbook on Computational Geometry, edited by J.R. Sack and J. Urrutia. A comprehensive overview is given of algorithms and data structures for proximity problems on point sets in IR D . In particular, the closest pair problem, th ..."
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Cited by 73 (13 self)
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This is the preliminary version of a chapter that will appear in the Handbook on Computational Geometry, edited by J.R. Sack and J. Urrutia. A comprehensive overview is given of algorithms and data structures for proximity problems on point sets in IR D . In particular, the closest pair problem
Closestpoint problems simplified on the RAM
 IN PROC. 13RD ACMSIAM SYMPOS. ON DISCRETE ALGORITHMS
, 2002
"... Basic proximity problems for lowdimensional point sets, such as closest pair (CP) and approximate nearest neighbor (ANN), have been studied extensively in the computational geometry literature, with well over a hundred papers published (we merely cite the survey by Smid [10] and omit most reference ..."
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Cited by 38 (4 self)
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Basic proximity problems for lowdimensional point sets, such as closest pair (CP) and approximate nearest neighbor (ANN), have been studied extensively in the computational geometry literature, with well over a hundred papers published (we merely cite the survey by Smid [10] and omit most
Optimal expectedtime algorithms for closest point problems
 ACM Transactions of Mathematical Software
, 1980
"... Geometric closest potnt problems deal with the proxLmity relationships in kdimensional point sets. Examples of closest point problems include building minimum spanning trees, nearest neighbor searching, and triangulation constructmn Shamos and Hoey [17] have shown how the Voronoi dtagram can be use ..."
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Cited by 95 (0 self)
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Geometric closest potnt problems deal with the proxLmity relationships in kdimensional point sets. Examples of closest point problems include building minimum spanning trees, nearest neighbor searching, and triangulation constructmn Shamos and Hoey [17] have shown how the Voronoi dtagram can
Efficient Parallel Algorithms for Closest Point Problems
, 1994
"... OF THE THESIS This dissertation develops and studies fast algorithms for solving closest point problems. Algorithms for such problems have applications in many areas including statistical classification, crystallography, data compression, and finite element analysis. In addition to a comprehensive e ..."
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OF THE THESIS This dissertation develops and studies fast algorithms for solving closest point problems. Algorithms for such problems have applications in many areas including statistical classification, crystallography, data compression, and finite element analysis. In addition to a comprehensive
Efficient parallel algorithms for closest point problems
, 1994
"... This dissertation develops and studies fast algorithms for solving closest point problems. Algorithms for such problems have applications in many areas including statistical classification, crystallography, data compression, and finite element analysis. In addition to a comprehensive empirical study ..."
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Cited by 11 (1 self)
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This dissertation develops and studies fast algorithms for solving closest point problems. Algorithms for such problems have applications in many areas including statistical classification, crystallography, data compression, and finite element analysis. In addition to a comprehensive empirical
New Techniques For Exact And Approximate Dynamic ClosestPoint Problems
, 1994
"... . Let S be a set of n points in IR D . It is shown that a range tree can be used to find an L1nearest neighbor in S of any query point, in O((logn) D\Gamma1 log log n) time. This data structure has size O(n(log n) D\Gamma1 ) and an amortized update time of O((logn) D\Gamma1 log log n). This result ..."
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Cited by 11 (2 self)
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is used to solve the (1 + ffl)approximate L 2 nearest neighbor problem within the same bounds (up to a constant factor that depends on ffl and D). In this o problem, for any query point p, a point q 2 S is computed such that the euclidean distance between p and q is at most (1 + ffl) times the euclidean
Closest Point Search in Lattices
 IEEE TRANS. INFORM. THEORY
, 2000
"... In this semitutorial paper, a comprehensive survey of closestpoint search methods for lattices without a regular structure is presented. The existing search strategies are described in a unified framework, and differences between them are elucidated. An efficient closestpoint search algorithm, ba ..."
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Cited by 324 (2 self)
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In this semitutorial paper, a comprehensive survey of closestpoint search methods for lattices without a regular structure is presented. The existing search strategies are described in a unified framework, and differences between them are elucidated. An efficient closestpoint search algorithm
Closestpoint queries for complex objects
"... In this paper we report on the implementation of a heuristic for computing the closest of a set of n given points in the plane to a complex query object, to wit a triangle, a circle, a rectangle etc. Our results indicate that the heuristic is effective for query objects with small perimeter relative ..."
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In this paper we report on the implementation of a heuristic for computing the closest of a set of n given points in the plane to a complex query object, to wit a triangle, a circle, a rectangle etc. Our results indicate that the heuristic is effective for query objects with small perimeter
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