Truly distribution-independent algorithms for the N-body problem

Aluru, None; Prabhu,; Gustafson,

doi:10.1109/superc.1994.344305

Cited by 7 publications

(13 citation statements)

References 15 publications

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“…Aluru et al discussed changing the tree structure of BarnesHut to improve performance [1]. We note that our transformations are independent of the type of tree used (indeed, the tree in raytracing is different from that in Barnes-Hut), and hence our approach can apply to their algorithm as well.…”

Section: Other Tree Traversal Transformationsmentioning

confidence: 99%

“…Pointer-based data structures are highly dynamic and the resulting memoryaccess patterns of applications that use them are highly input-dependent and unpredictable. As a result, the standard techniques for reasoning about locality in regular applications are simply inapplicable 1 . The apparent lack of structure in irregular programs can be misleading.…”

Section: Introductionmentioning

confidence: 99%

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Enhancing locality for recursive traversals of recursive structures

JoYoungjoon

KulkarniMilind

2011

SIGPLAN Not.

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While there has been decades of work on developing automatic, locality-enhancing transformations for regular programs that operate over dense matrices and arrays, there has been little investigation of such transformations for irregular programs, which operate over pointer-based data structures such as graphs, trees and lists. In this paper, we argue that, for a class of irregular applications we call traversal codes, there exists substantial data reuse and hence opportunity for locality exploitation.We develop a novel optimization called point blocking, inspired by the classic tiling loop transformation, and show that it can substantially enhance temporal locality in traversal codes. We then present a transformation and optimization framework called TreeTiler that automatically detects opportunities for applying point blocking and applies the transformation. TreeTiler uses autotuning techniques to determine appropriate parameters for the transformation. For a series of traversal algorithms drawn from real-world applications, we show that TreeTiler is able to deliver performance improvements of up to 245% over an optimized (but non-transformed) parallel baseline, and in several cases, significantly better scalability.

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Section: Other Tree Traversal Transformationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Enhancing locality for recursive traversals of recursive structures

JoYoungjoon

KulkarniMilind

2011

SIGPLAN Not.

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“…Aluru et al [1] has shown that the running time of adaptive FMM using quad tree [16] depends on the particle distribution and cannot be bounded in number of particles. In order to remedy this and guarantee O(|V |log|V |) running time complexity, [18] uses complicated tree thinning and balancing techniques.…”

Section: Processing the K-d Treementioning

confidence: 99%

Rapid Multipole Graph Drawing on the GPU

Godiyal

Hoberock

Garland

et al. 2009

Lecture Notes in Computer Science

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Abstract. As graphics processors become powerful, ubiquitous and easier to program, they have also become more amenable to general purpose high-performance computing, including the computationally expensive task of drawing large graphs. This paper describes a new parallel analysis of the multipole method of graph drawing to support its efficient GPU implementation. We use a variation of the Fast Multipole Method to estimate the long distance repulsive forces in force directed layout. We support these multipole computations efficiently with a k-d tree constructed and traversed on the GPU. The algorithm achieves impressive speedup over previous CPU and GPU methods, drawing graphs with hundreds of thousands of vertices within a few seconds via CUDA on an NVIDIA GeForce 8800 GTX.

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“…The computational effort for the determination of the tree for such highly nonuniform systems scales as N(logN) 4 as shown by Aluru and co-workers. 27,28 The number density of particles in most suspension problems is typically large and the probability of developing a highly nonuniform suspension is generally small. In few exceptional cases, such as gas-solid fluidized bed where large voids devoid of any particles may form, creating tree with nonuniform m lev may prove useful.…”

Section: An O(n) Algorithmmentioning

confidence: 99%

An O(N) algorithm for Stokes and Laplace interactions of particles

Sangani

1996

Physics of Fluids

121

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A method for computing Laplace and Stokes interactions among N spherical particles arbitrarily placed in a unit cell of a periodic array is described. The method is based on an algorithm by Greengard and Rokhlin [J. Comput. Phys. 73, 325 (1987)] for rapidly summing the Laplace interactions among particles by organizing the particles into a number of different groups of varying sizes. The far-field induced by each group of particles is expressed by a multipole expansion technique into an equivalent field with its singularities at the center of the group. The resulting computational effort increases only linearly with N. The method is applied to a number of problems in suspension mechanics with the goal of assessing the efficiency and the potential usefulness of the method in studying dynamics of large systems. It is shown that reasonably accurate results for the interaction forces are obtained in most cases even with relatively low-order multipole expansions.

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Truly distribution-independent algorithms for the N-body problem

Cited by 7 publications

References 15 publications

Enhancing locality for recursive traversals of recursive structures

Enhancing locality for recursive traversals of recursive structures

Rapid Multipole Graph Drawing on the GPU

An O(N) algorithm for Stokes and Laplace interactions of particles

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