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Divided k-d Trees

by Marc J. van Kreveld, Mark H. Overmars , 1989
"... A variant of k-d trees, the divided k-d tree, is described that has some important advantages over ordinary k-d trees. The divided k-d tree is fully dynamic and allows for the insertion and deletion of points in O(log n) worst-case time. Moreover, divided k-d trees allow for split and concatenate op ..."
Abstract - Cited by 9 (0 self) - Add to MetaCart
A variant of k-d trees, the divided k-d tree, is described that has some important advantages over ordinary k-d trees. The divided k-d tree is fully dynamic and allows for the insertion and deletion of points in O(log n) worst-case time. Moreover, divided k-d trees allow for split and concatenate

Squarish k-d trees

by Luc Devroye, Jean Jabbour, Carlos Zamora-cura - SIAM JOURNAL ON COMPUTING , 2000
"... We modify the k-d tree on [0, 1] d by always cutting the longest edge instead of rotating through the coordinates. This modification makes the expected time behavior of lower-dimensional partial match queries behave as for perfectly balanced complete k-d trees on n nodes. This is in contrast to a ..."
Abstract - Cited by 8 (3 self) - Add to MetaCart
We modify the k-d tree on [0, 1] d by always cutting the longest edge instead of rotating through the coordinates. This modification makes the expected time behavior of lower-dimensional partial match queries behave as for perfectly balanced complete k-d trees on n nodes. This is in contrast to a

Distributed k-d Trees

by Enrico Nardelli - In Proceedings 16th Conference of Chilean Computer Science Society (SCCC’96 , 1996
"... In this paper we present a generalization of the k-d tree data structure suitable for an efficient management and querying in a distributed framework. We present optimal searching algorithm for exact, partial, and range search queries. Optimality is in the sense that (1) only servers that could have ..."
Abstract - Cited by 12 (4 self) - Add to MetaCart
In this paper we present a generalization of the k-d tree data structure suitable for an efficient management and querying in a distributed framework. We present optimal searching algorithm for exact, partial, and range search queries. Optimality is in the sense that (1) only servers that could

Fast Ray Tracing Using K-D Trees

by Donald Fussell, K. R. Subramanian , 1988
"... A hierarchical search structure for ray tracing based on k-d trees is introduced. This data ..."
Abstract - Cited by 13 (0 self) - Add to MetaCart
A hierarchical search structure for ray tracing based on k-d trees is introduced. This data

Approximate k-d tree search for efficient ICP

by Michael Greenspan, Mike Yurick - In Fourth International Conference on 3-D Digital Imaging and Modeling (3DIM ’03 , 2003
"... A method is presented that uses an Approximate Nearest Neighbor method for determining correspondences within the Iterative Closest Point Algorithm. The method is based upon the k-d tree. The standard k-d tree uses a tentative backtracking search to identify nearest neighbors. In contrast, the Appro ..."
Abstract - Cited by 34 (0 self) - Add to MetaCart
A method is presented that uses an Approximate Nearest Neighbor method for determining correspondences within the Iterative Closest Point Algorithm. The method is based upon the k-d tree. The standard k-d tree uses a tentative backtracking search to identify nearest neighbors. In contrast

Parallel SAH k-D Tree Construction

by M. Doggett, S. Laine, W. Hunt (editors, Byn Choi, Rakesh Komuravelli, Victor Lu, Hyojin Sung, Robert L. Bocchino, Sarita V. Adve, John C. Hart
"... The k-D tree is a well-studied acceleration data structure for ray tracing. It is used to organize primitives in a scene to allow efficient execution of intersection operations between rays and the primitives. The highest quality k-D tree can be obtained using greedy cost optimization based on a sur ..."
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The k-D tree is a well-studied acceleration data structure for ray tracing. It is used to organize primitives in a scene to allow efficient execution of intersection operations between rays and the primitives. The highest quality k-D tree can be obtained using greedy cost optimization based on a

Parallel Architecture for k–d Trees

by Geoffrey A. Frank, Donald F. Stanat Dtic, Geoffrey A. Frank, Donald F. Stanat , 1988
"... We describe a special purpose computer architecture for the parallel processing of queries, including associative searches, in a dynamic file. The architecture is a highly-parallel network of small processors of two types connected in a full binary tree network. Records are stored in the leaves of t ..."
Abstract - Cited by 2 (0 self) - Add to MetaCart
to the records for which it is responsible. File updates cause a reorganization of the tree, which is accomplished in a manner that can accommodate either incremental or massive changes. The architecture can be viewed as a hardware implementation of Bentley's k-d trees. The design is extensible and well

Cached k-d tree search for ICP algorithms

by Andreas Nüchter, Kai Lingemann, Joachim Hertzberg
"... The ICP (Iterative Closest Point) algorithm is the de facto standard for geometric alignment of threedimensional models when an initial relative pose estimate is available. The basis of ICP is the search for closest points. Since the development of ICP, k-d trees have been used to accelerate the sea ..."
Abstract - Cited by 14 (1 self) - Add to MetaCart
The ICP (Iterative Closest Point) algorithm is the de facto standard for geometric alignment of threedimensional models when an initial relative pose estimate is available. The basis of ICP is the search for closest points. Since the development of ICP, k-d trees have been used to accelerate

Optimizing Search Strategies in k-d Trees

by Neal Sample, Matthew Haines, Mark Arnold, Timothy Purcell , 2001
"... K-d trees have been widely studied, yet their complete advantages are often not realized due to ineffective search implementations and degrading performance in high dimensional spaces. We outline an effective search algorithm for k-d trees that combines an optimal depth-first branch and bound (DFBB) ..."
Abstract - Cited by 4 (0 self) - Add to MetaCart
K-d trees have been widely studied, yet their complete advantages are often not realized due to ineffective search implementations and degrading performance in high dimensional spaces. We outline an effective search algorithm for k-d trees that combines an optimal depth-first branch and bound (DFBB

Analysis of Range Search for Random K-D Trees

by Philippe Chanzy, Luc Devroye, Carlos Zamora-cura - Acta Informatica , 1999
"... . We analyze the expected time complexity of range searching with k-d trees in all dimensions when the data points are uniformly distributed in the unit hypercube. The partial match results of Flajolet and Puech are reproved using elementary probabilistic methods. In addition, we give asymptotic exp ..."
Abstract - Cited by 10 (2 self) - Add to MetaCart
. We analyze the expected time complexity of range searching with k-d trees in all dimensions when the data points are uniformly distributed in the unit hypercube. The partial match results of Flajolet and Puech are reproved using elementary probabilistic methods. In addition, we give asymptotic
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