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Approximate Range Searching
 in Proc. 11th Annu. ACM Sympos. Comput. Geom
, 1995
"... The range searching problem is a fundamental problem in computational geometry, with numerous important applications. Most research has focused on solving this problem exactly, but lower bounds show that if linear space is assumed, the problem cannot be solved in polylogarithmic time, except for the ..."
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Cited by 92 (20 self)
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The range searching problem is a fundamental problem in computational geometry, with numerous important applications. Most research has focused on solving this problem exactly, but lower bounds show that if linear space is assumed, the problem cannot be solved in polylogarithmic time, except
Approximate range searching in higher dimension
, 2008
"... Applying standard dimensionality reduction techniques, we show how to perform approximate range searching in higher dimension while avoiding the curse of dimensionality. Given n points in a unit ball in Rd, an approximate halfspace range query counts (or reports) the points in a query halfspace; t ..."
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Cited by 9 (0 self)
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Applying standard dimensionality reduction techniques, we show how to perform approximate range searching in higher dimension while avoiding the curse of dimensionality. Given n points in a unit ball in Rd, an approximate halfspace range query counts (or reports) the points in a query halfspace
Approximate Range Searching in External Memory
"... Abstract. In this paper, we present two linearsize external memory data structures for approximate range searching. Our first structure, the BARBtree, stores a set of N points in R d and can report all points inside a query range Q by accessing O(log B N + ɛ γ + kɛ/B) disk blocks, where B is the ..."
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Abstract. In this paper, we present two linearsize external memory data structures for approximate range searching. Our first structure, the BARBtree, stores a set of N points in R d and can report all points inside a query range Q by accessing O(log B N + ɛ γ + kɛ/B) disk blocks, where B
Approximate Range Searching: The Absolute Modely
, 2010
"... Range searching is a well known problem in the area of geometric data structures. We consider this problem in the context of approximation, where an approximation parameter "> 0 is provided. Most prior work on this problem has focused on the case of relative errors, where each range shape R ..."
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Range searching is a well known problem in the area of geometric data structures. We consider this problem in the context of approximation, where an approximation parameter "> 0 is provided. Most prior work on this problem has focused on the case of relative errors, where each range shape R
Approximate Range Searching: The Absolute Model
 COMPUTATIONAL GEOMETRY: THEORY AND APPLICATIONS
, 2009
"... ..."
Approximate Range Searching Using Binary Space Partitions
"... We show how any BSP tree TP for the endpoints of a set of n disjoint segments in the plane can be used to obtain a BSP tree of size O(n · depth(TP)) for the segments themselves, such that the rangesearching efficiency remains almost the same. We apply this technique to obtain a BSP tree of size O(n ..."
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Cited by 11 (3 self)
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(n log n) such that εapproximate range searching queries with any constantcomplexity convex query range can be answered in O(minε>0{(1/ε) + kε} log n) time, where kε is the number of segments intersecting the εextended range. The same result can be obtained for disjoint constantcomplexity curves
The effect of corners on the complexity of approximate range searching
 DISCRETE COMPUT GEOM (2009 ) 41 : 398–443 399
, 2009
"... Given an nelement point set in R d, the range searching problem involves preprocessing these points so that the total weight, or for our purposes the semigroup sum, of the points lying within a given query range η can be determined quickly. In εapproximate range searching we assume that η is bound ..."
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Cited by 11 (6 self)
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Given an nelement point set in R d, the range searching problem involves preprocessing these points so that the total weight, or for our purposes the semigroup sum, of the points lying within a given query range η can be determined quickly. In εapproximate range searching we assume that η
Abstract Efficient Spatial Indexes for Approximate Range Searching
"... Building efficient spatial indexes for range searching is a central problem in spatial databases. The Rtree has been a popular spatial index thanks to its simplicity, ability to answer various queries, and the flexibility to store spatial objects of different shapes. However, the Rtree is known to ..."
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to be a heuristicbased structure and no guarantees can be made on its query performance. In this paper, we present two diskbased indexes for approximate range searching that are as versatile as the Rtree, and at the same time provide good guarantees on the query performance, albeit in the approximate
Efficient Spatial Indexes for Approximate Range Searching
"... Building efficient spatial indexes for range searching is a central problem in spatial databases. The Rtree has been a popular spatial index thanks to its simplicity, ability to answer various queries, and the flexibility to store spatial objects of different shapes. However, the Rtree is known to ..."
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to be a heuristicbased structure and no guarantees can be made on its query performance. In this paper, we present two diskbased indexes for approximate range searching that are as versatile as the Rtree, and at the same time provide good guarantees on the query performance, albeit in the approximate
Approximate Range Searching In The Absolute Error Model
, 2007
"... Range searching is a well known problem in computational geometry. We consider this problem in the context of approximation, where an approximation parameter ε > 0 is provided. Most prior work on this problem has focused on the relative error model, where each range shape R is bounded, and points ..."
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Cited by 2 (2 self)
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Range searching is a well known problem in computational geometry. We consider this problem in the context of approximation, where an approximation parameter ε > 0 is provided. Most prior work on this problem has focused on the relative error model, where each range shape R is bounded
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