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Packing hyperspheres in highdimensional Euclidean spaces
, 2007
"... We present a study of disordered jammed hardsphere packings in four, five, and sixdimensional Euclidean spaces. Using a collisiondriven packing generation algorithm, we obtain the first estimates for the packing fractions of the maximally random jammed �MRJ � states for space dimensions d=4, 5, ..."
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Cited by 13 (2 self)
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We present a study of disordered jammed hardsphere packings in four, five, and sixdimensional Euclidean spaces. Using a collisiondriven packing generation algorithm, we obtain the first estimates for the packing fractions of the maximally random jammed �MRJ � states for space dimensions d=4, 5
Reporting Neighbors in HighDimensional Euclidean Space
"... We consider the following problem, which arises in many database and webbased applications: Given a set P of n points in a highdimensional space Rd and a distance r, we want to report all pairs of points of P at Euclidean distance at most r. We present two randomized algorithms, one based on rando ..."
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Cited by 5 (1 self)
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We consider the following problem, which arises in many database and webbased applications: Given a set P of n points in a highdimensional space Rd and a distance r, we want to report all pairs of points of P at Euclidean distance at most r. We present two randomized algorithms, one based
HOMOLOGY OF MODULI SPACES OF LINKAGES IN HIGHDIMENSIONAL EUCLIDEAN SPACE
"... We study the topology of moduli spaces of closed linkages in R d depending on a length vector ℓ ∈ R n. In particular, we use equivariant Morse theory to obtain information on the homology groups of these spaces, which works best for odd d. In the case d = 5 we calculate the Poincaré polynomial in te ..."
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Cited by 2 (2 self)
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We study the topology of moduli spaces of closed linkages in R d depending on a length vector ℓ ∈ R n. In particular, we use equivariant Morse theory to obtain information on the homology groups of these spaces, which works best for odd d. In the case d = 5 we calculate the Poincaré polynomial
On Computing the Diameter of a Point Set in High Dimensional Euclidean Space
, 2000
"... . We consider the problem of computing the diameter of a set of n points in ddimensional Euclidean space under Euclidean distance function. We describe an algorithm that in time O(dn log n + n 2 ) finds with high probability an arbitrarily close approximation of the diameter. For large values of ..."
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Cited by 1 (0 self)
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. We consider the problem of computing the diameter of a set of n points in ddimensional Euclidean space under Euclidean distance function. We describe an algorithm that in time O(dn log n + n 2 ) finds with high probability an arbitrarily close approximation of the diameter. For large values
SRS: Solving cApproximate Nearest Neighbor Queries in High Dimensional Euclidean Space with a Tiny Index
"... Nearest neighbor searches in highdimensional space have many important applications in domains such as data mining, and multimedia databases. The problem is challenging due to the phenomenon called “curse of dimensionality”. An alternative solution is to consider algorithms that returns a capprox ..."
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Cited by 1 (1 self)
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Nearest neighbor searches in highdimensional space have many important applications in domains such as data mining, and multimedia databases. The problem is challenging due to the phenomenon called “curse of dimensionality”. An alternative solution is to consider algorithms that returns a c
Probabilistic Roadmaps for Path Planning in HighDimensional Configuration Spaces
 IEEE INTERNATIONAL CONFERENCE ON ROBOTICS AND AUTOMATION
, 1996
"... A new motion planning method for robots in static workspaces is presented. This method proceeds in two phases: a learning phase and a query phase. In the learning phase, a probabilistic roadmap is constructed and stored as a graph whose nodes correspond to collisionfree configurations and whose edg ..."
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Cited by 1277 (120 self)
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A new motion planning method for robots in static workspaces is presented. This method proceeds in two phases: a learning phase and a query phase. In the learning phase, a probabilistic roadmap is constructed and stored as a graph whose nodes correspond to collisionfree configurations and whose edges correspond to feasible paths between these configurations. These paths are computed using a simple and fast local planner. In the query phase, any given start and goal configurations of the robot are connected to two nodes of the roadmap; the roadmap is then searched for a path joining these two nodes. The method is general and easy to implement. It can be applied to virtually any type of holonomic robot. It requires selecting certain parameters (e.g., the duration of the learning phase) whose values depend on the scene, that is the robot and its workspace. But these values turn out to be relatively easy to choose, Increased efficiency can also be achieved by tailoring some components of the method (e.g., the local planner) to the considered robots. In this paper the method is applied to planar articulated robots with many degrees of freedom. Experimental results show that path planning can be done in a fraction of a second on a contemporary workstation (=150 MIPS), after learning for relatively short periods of time (a few dozen seconds)
The Xtree: An index structure for highdimensional data
 In Proceedings of the Int’l Conference on Very Large Data Bases
, 1996
"... In this paper, we propose a new method for indexing large amounts of point and spatial data in highdimensional space. An analysis shows that index structures such as the R*tree are not adequate for indexing highdimensional data sets. The major problem of Rtreebased index structures is the over ..."
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Cited by 592 (17 self)
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In this paper, we propose a new method for indexing large amounts of point and spatial data in highdimensional space. An analysis shows that index structures such as the R*tree are not adequate for indexing highdimensional data sets. The major problem of Rtreebased index structures
Estimating the Support of a HighDimensional Distribution
, 1999
"... Suppose you are given some dataset drawn from an underlying probability distribution P and you want to estimate a "simple" subset S of input space such that the probability that a test point drawn from P lies outside of S is bounded by some a priori specified between 0 and 1. We propo ..."
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Cited by 783 (29 self)
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Suppose you are given some dataset drawn from an underlying probability distribution P and you want to estimate a "simple" subset S of input space such that the probability that a test point drawn from P lies outside of S is bounded by some a priori specified between 0 and 1. We
An equipartition property for highdimensional logconcave distributions
"... AbstractA new effective equipartition property for logconcave distributions on highdimensional Euclidean spaces is described, and some applications are sketched. ..."
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AbstractA new effective equipartition property for logconcave distributions on highdimensional Euclidean spaces is described, and some applications are sketched.
Results 1  10
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