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203
Multidimensional Access Methods
, 1998
"... Search operations in databases require special support at the physical level. This is true for conventional databases as well as spatial databases, where typical search operations include the point query (find all objects that contain a given search point) and the region query (find all objects that ..."
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Cited by 671 (3 self)
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Search operations in databases require special support at the physical level. This is true for conventional databases as well as spatial databases, where typical search operations include the point query (find all objects that contain a given search point) and the region query (find all objects that overlap a given search region).
The quadtree and related hierarchical data structures
 ACM Computing Surveys
, 1984
"... A tutorial survey is presented of the quadtree and related hierarchical data structures. They are based on the principle of recursive decomposition. The emphasis is on the representation of data used in applications in image processing, computer graphics, geographic information systems, and robotics ..."
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Cited by 515 (11 self)
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A tutorial survey is presented of the quadtree and related hierarchical data structures. They are based on the principle of recursive decomposition. The emphasis is on the representation of data used in applications in image processing, computer graphics, geographic information systems, and robotics. There is a greater emphasis on region data (i.e., twodimensional shapes) and to a lesser extent on point, curvilinear, and threedimensional data. A number of operations in which such data structures find use are examined in greater detail.
Spatial Data Structures
, 1995
"... An overview is presented of the use of spatial data structures in spatial databases. The focus is on hierarchical data structures, including a number of variants of quadtrees, which sort the data with respect to the space occupied by it. Suchtechniques are known as spatial indexing methods. Hierarch ..."
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Cited by 322 (13 self)
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An overview is presented of the use of spatial data structures in spatial databases. The focus is on hierarchical data structures, including a number of variants of quadtrees, which sort the data with respect to the space occupied by it. Suchtechniques are known as spatial indexing methods. Hierarchical data structures are based on the principle of recursive decomposition. They are attractive because they are compact and depending on the nature of the data they save space as well as time and also facilitate operations such as search. Examples are given of the use of these data structures in the representation of different data types such as regions, points, rectangles, lines, and volumes.
An Introduction to Spatial Database Systems
 THE VLDB JOURNAL
, 1994
"... We propose a definition of a spatial database system as a database system that offers spatial data types in its data model and query language, and supports ..."
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Cited by 211 (9 self)
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We propose a definition of a spatial database system as a database system that offers spatial data types in its data model and query language, and supports
Designing pixeloriented visualization techniques: Theory and applications
 IEEE Transactions on Visualization and Computer Graphics
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Visualization Techniques for Mining Large Databases: A Comparison
 IEEE Transactions on Knowledge and Data Engineering
, 1996
"... Visual data mining techniques have proven to be of high value in exploratory data analysis and they also have a high potential for mining large databases. In this article, we describe and evaluate a new visualizationbased approach to mining large databases. The basic idea of our visual data mining ..."
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Cited by 104 (1 self)
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Visual data mining techniques have proven to be of high value in exploratory data analysis and they also have a high potential for mining large databases. In this article, we describe and evaluate a new visualizationbased approach to mining large databases. The basic idea of our visual data mining techniques is to represent as many data items as possible on the screen at the same time by mapping each data value to a pixel of the screen and arranging the pixels adequately. The major goal of this article is to evaluate our visual data mining techniques and to compare them to other wellknown visualization techniques for multidimensional data: the parallel coordinate and stick figure visualization techniques. For the evaluation of visual data mining techniques, in the first place the perception of properties of the data counts, and only in the second place the CPU time and the number of secondary storage accesses are important. In addition to testing the visualization techniques using re...
Scalable Network Distance Browsing in Spatial Databases
, 2008
"... An algorithm is presented for finding the k nearest neighbors in a spatial network in a bestfirst manner using network distance. The algorithm is based on precomputing the shortest paths between all possible vertices in the network and then making use of an encoding that takes advantage of the fact ..."
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Cited by 79 (8 self)
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An algorithm is presented for finding the k nearest neighbors in a spatial network in a bestfirst manner using network distance. The algorithm is based on precomputing the shortest paths between all possible vertices in the network and then making use of an encoding that takes advantage of the fact that the shortest paths from vertex u to all of the remaining vertices can be decomposed into subsets based on the first edges on the shortest paths to them from u. Thus, in the worst case, the amount of work depends on the number of objects that are examined and the number of links on the shortest paths to them from q, rather than depending on the number of vertices in the network. The amount of storage required to keep track of the subsets is reduced by taking advantage of their spatial coherence which is captured by the aid of a shortest path quadtree. In particular, experiments on a number of large road networks as
High Resolution Forward and Inverse Earthquake Modeling on Terascale Computers
 In SC2003
, 2003
"... For earthquake simulations to play an important role in the reduction of seismic risk, they must be capable of high resolution and high fidelity. We have developed algorithms and tools for earthquake simulation based on multiresolution hexahedral meshes. We have used this capability to carry out 1 H ..."
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Cited by 73 (24 self)
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For earthquake simulations to play an important role in the reduction of seismic risk, they must be capable of high resolution and high fidelity. We have developed algorithms and tools for earthquake simulation based on multiresolution hexahedral meshes. We have used this capability to carry out 1 Hz simulations of the 1994 Northridge earthquake in the LA Basin using 100 million grid points. Our wave propagation solver sustains 1.21 teraflop/s for 4 hours on 3000 AlphaServer processors at 80% parallel efficiency. Because of uncertainties in characterizing earthquake source and basin material properties, a critical remaining challenge is to invert for source and material parameter fields for complex 3D basins from records of past earthquakes. Towards this end, we present results for material and source inversion of highresolution models of basins undergoing antiplane motion using parallel scalable inversion algorithms that overcome many of the difficulties particular to inverse heterogeneous wave propagation problems.
O.: p4est: scalable algorithms for parallel adaptive mesh refinement on forests of octrees
 SIAM J. Sci. Comput. (in press
"... Abstract. We present scalable algorithms for parallel adaptive mesh refinement and coarsening (AMR), partitioning, and 2:1 balancing on computational domains composed of multiple connected 2D quadtrees or 3D octrees, referred to as a forest of octrees. By distributing the union of octants from all o ..."
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Cited by 37 (5 self)
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Abstract. We present scalable algorithms for parallel adaptive mesh refinement and coarsening (AMR), partitioning, and 2:1 balancing on computational domains composed of multiple connected 2D quadtrees or 3D octrees, referred to as a forest of octrees. By distributing the union of octants from all octrees in parallel, we combine the high scalability proven previously for adaptive singleoctree algorithms with the geometric flexibility that can be achieved by arbitrarily connected hexahedral macromeshes, in which each macroelement is the root of an adapted octree. A key concept of our approach is an encoding scheme of the interoctree connectivity that permits arbitrary relative orientations between octrees. Based on this encoding we develop interoctree transformations of octants. These form the basis for highlevel parallel octree algorithms, which are designed to interact with an application code such as a numerical solver for partial differential equations. We have implemented and tested these algorithms in the p4est software library. We demonstrate the parallel scalability of p4est on its own and in combination with two geophysics codes. Using p4est we generate and adapt multioctree meshes with up to 5.13 × 1011 octants on as many as 220,320 CPU cores and execute the 2:1 balance algorithm in less than 10 seconds per million octants per process. Key words. forest of octrees, parallel adaptive mesh refinement, Morton code, scalable algorithms, largescale scientific computing
A Fast Similarity Join Algorithm Using Graphics Processing Units
"... Abstract — A similarity join operation A ⋊⋉ɛ B takes two sets of points A, B and a value ɛ ∈ R, and outputs pairs of points p ∈ A, q ∈ B, such that the distance D(p, q) ≤ ɛ. Similarity joins find use in a variety of fields, such as clustering, text mining, and multimedia databases. A novel similari ..."
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Cited by 35 (1 self)
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Abstract — A similarity join operation A ⋊⋉ɛ B takes two sets of points A, B and a value ɛ ∈ R, and outputs pairs of points p ∈ A, q ∈ B, such that the distance D(p, q) ≤ ɛ. Similarity joins find use in a variety of fields, such as clustering, text mining, and multimedia databases. A novel similarity join algorithm called LSS is presented that executes on a Graphics Processing Unit (GPU), exploiting its parallelism and high data throughput. As GPUs only allow simple data operations such as the sorting and searching of arrays, LSS uses these two operations to cast a similarity join operation as a GPU sortandsearch problem. It first creates, on the fly, a set of spacefilling curves on one of its input datasets, using a parallel GPU sort routine. Next, LSS processes each point p of the other dataset in parallel. For each p, it searches an interval of one of the spacefilling curves guaranteed to contain all the pairs in which p participates. Using extensive theoretical and experimental analysis, LSS is shown to offer a good balance between time and work efficiency. Experimental results demonstrate that LSS is suitable for similarity joins in large highdimensional datasets, and that it performs well when compared against two existing prominent similarity join methods. I.