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The Skip Quadtree: A Simple Dynamic Data Structure for Multidimensional Data
, 2005
"... We present a new multidimensional data structure, which we call the skip quadtree (for point data in R²) or the skip octree (for point data in R d, with constant d> 2). Our data structure combines the best features of two wellknown data structures, in that it has the welldefined “box”shaped regi ..."
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Cited by 33 (4 self)
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We present a new multidimensional data structure, which we call the skip quadtree (for point data in R²) or the skip octree (for point data in R d, with constant d> 2). Our data structure combines the best features of two wellknown data structures, in that it has the welldefined “box”shaped regions of region quadtrees and the logarithmicheight search and update hierarchical structure of skip lists. Indeed, the bottom level of our structure is exactly a region quadtree (or octree for higher dimensional data). We describe efficient algorithms for inserting and deleting points in a skip quadtree, as well as fast methods for performing point location, approximate range, and approximate nearest neighbor queries.
Efficient Parallel Algorithms and Software for Compressed Octrees with Applications to Hierarchical Methods
 High Performance Computing  HiPC 2001 8th International Conference
"... Abstract. We describe the design and implementation of efficient parallel algorithms, and a software library for the parallel implementation of compressed octree data structures. Octrees are widely used in supporting hierarchical methods for scientific applications such as the Nbody problem, molecu ..."
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Cited by 8 (0 self)
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Abstract. We describe the design and implementation of efficient parallel algorithms, and a software library for the parallel implementation of compressed octree data structures. Octrees are widely used in supporting hierarchical methods for scientific applications such as the Nbody problem, molecular dynamics and smoothed particle hydrodynamics. The primary goal of our work is to identify and abstract the commonalities present in various hierarchical methods using octrees, design efficient parallel algorithms for them, and encapsulate them in a software library. We designed provably efficient parallel algorithms and implementation strategies that perform well irrespective of data distribution. The library will enable rapid development of applications, allowing application developers to use efficient parallel algorithms developed for this purpose, without the necessity of having detailed knowledge of the algorithms or of implementing them. The software is developed in C using the Message Passing Interface (MPI). We report experimental results on an IBM SP and a Pentium cluster. 1
An Automatic Loadbalanced Parallel Multilevel Fast Multipole Method For Large Scale Electromagnetic Scattering Problem
"... Abstract—A parallel multilevel fast multipole method for computing the large scale electromagnetic scattering problem is proposed and implemented in this paper. In recent years, multilevel fast multipole method (MLFMA) has been widely used for analyzing electromagnetic scattering problem of electric ..."
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Abstract—A parallel multilevel fast multipole method for computing the large scale electromagnetic scattering problem is proposed and implemented in this paper. In recent years, multilevel fast multipole method (MLFMA) has been widely used for analyzing electromagnetic scattering problem of electric large object. In order to extend the range of problem that can be solved using this algorithm, we implement a parallel fast multipole method which can run on the distributed memory computer system. This parallel algorithm is based on the Messagepassing Interface (MPI). A compressed octree based parallel domain subdivision algorithm is used for efficiently avoiding the load balance problem between different CPUs which is caused by the irregular object shape. The parallel efficiency of this algorithm is demonstrated by different computing examples. We have solved electromagnetic scattering problem of many practicality military targets with more than 5,000,000 unknowns using our parallel multilevel fast multipole code on Drawing 4000A SuperComputer at Shanghai SuperComputing Center.
Squarepants in a Tree: Sum of Subtree Clustering and Hyperbolic Pants Decomposition
, 2006
"... Abstract. We provide efficient constant factor approximation algorithms for the problems of finding a hierarchical clustering of a point set in any metric space, minimizing the sum of minimimum spanning tree lengths within each cluster, and in the hyperbolic or Euclidean planes, minimizing the sum o ..."
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Abstract. We provide efficient constant factor approximation algorithms for the problems of finding a hierarchical clustering of a point set in any metric space, minimizing the sum of minimimum spanning tree lengths within each cluster, and in the hyperbolic or Euclidean planes, minimizing the sum of cluster perimeters. Our algorithms for the hyperbolic and Euclidean planes can also be used to provide a pants decomposition, that is, a set of disjoint simple closed curves partitioning the plane minus the input points into subsets with exactly three boundary components, with approximately minimum total length. In the Euclidean case, these curves are squares; in the hyperbolic case, they combine our Euclidean square pants decomposition with our tree clustering method for general metric spaces. 1