Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of the same cluster and comparatively few edges joining vertices of different clusters. Such clusters, or communities, can be considered as fairly independent compartments of a graph, playing a similar role like, e. g., the tissues or the organs in the human body. Detecting communities is of great importance in sociology, biology and computer science, disciplines where systems are often represented as graphs. This problem is very hard and not yet satisfactorily solved, despite the huge effort of a large interdisciplinary community of scientists working on it over the past few years. We will attempt a thorough exposition of the topic, from the definition of the main elements of the problem, to the presentation of most methods developed, with a special focus on techniques designed by statistical physicists, from the discussion of crucial issues like the significance of clustering and how methods should be tested and compared against each other, to the description of applications to real networks.

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Community detection in graphs

We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

Many applications in computer graphics require complex, highly detailed models. However, the level of detail actually necessary may vary considerably. To control processing time, it is often desirable to use approximations in place of excessively detailed models. We have developed a surface simplification algorithm which can rapidly produce high quality approximations of polygonal models. The algorithm uses iterative contractions of vertex pairs to simplify models and maintains surface error approximations using quadric matrices. By contracting arbitrary vertex pairs (not just edges), our algorithm is able to join unconnected regions of models. This can facilitate much better approximations, both visually and with respect to geometric error. In order to allow topological joining, our system also supports non-manifold surface models. CR Categories: I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—surface and object representations

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Surface simplification using quadric error metrics

We describe the design of high-performance parallel radix sort and merge sort routines for manycore GPUs, taking advantage of the full programmability offered by CUDA. Our radix sort is the fastest GPU sort and our merge sort is the fastest comparison-based sort reported in the literature. Our radix sort is up to 4 times faster than the graphics-based GPUSort and greater than 2 times faster than other CUDA-based radix sorts. It is also 23% faster, on average, than even a very carefully optimized multicore CPU sorting routine. To achieve this performance, we carefully design our algorithms to expose substantial fine-grained parallelism and decompose the computation into independent tasks that perform minimal global communication. We exploit the high-speed onchip shared memory provided by NVIDIA's GPU architecture and efficient data-parallel primitives, particularly parallel scan. While targeted at GPUs, these algorithms should also be well-suited for other manycore processors.

/pdf/designing-efficient-sorting-algorithms-for-manycore-gpus-117bn8t8yu.pdf

Designing efficient sorting algorithms for manycore GPUs

This article discusses the capabilities of state-of-the art GPU-based high-throughput computing systems and considers the challenges to scaling single-chip parallel-computing systems, highlighting high-impact areas that the computing research community can address. Nvidia Research is investigating an architecture for a heterogeneous high-performance computing system that seeks to address these challenges.

GPUs and the Future of Parallel Computing

: This paper surveys methods for simplifying and approximating polygonal surfaces. A polygonal surface is a piecewise-linear surface in 3-D defined by a set of polygons; typically a set of triangles. Methods from computer graphics, computer vision, cartography, computational geometry, and other fields are classified, summarized, and compared both practically and theoretically. The surface types range from height fields (bivariate functions), to manifolds, to non-manifold self-intersecting surfaces. Piecewise-linear curve simplification is also briefly surveyed.

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Survey of Polygonal Surface Simplification Algorithms

Breadth-first search (BFS) is a core primitive for graph traversal and a basis for many higher-level graph analysis algorithms. It is also representative of a class of parallel computations whose memory accesses and work distribution are both irregular and data-dependent. Recent work has demonstrated the plausibility of GPU sparse graph traversal, but has tended to focus on asymptotically inefficient algorithms that perform poorly on graphs with non-trivial diameter.We present a BFS parallelization focused on fine-grained task management constructed from efficient prefix sum that achieves an asymptotically optimal O(|V|+|E|) work complexity. Our implementation delivers excellent performance on diverse graphs, achieving traversal rates in excess of 3.3 billion and 8.3 billion traversed edges per second using single and quad-GPU configurations, respectively. This level of performance is several times faster than state-of-the-art implementations both CPU and GPU platforms.

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Scalable GPU graph traversal

The CUDA programming model provides a straightforward means of describing inherently parallel computations, and NVIDIA's Tesla GPU architecture delivers high computational throughput on massively parallel problems. This article surveys experiences gained in applying CUDA to a diverse set of problems and the parallel speedups over sequential codes running on traditional CPU architectures attained by executing key computations on the GPU.

Michael Garland

Papers

Designing efficient sorting algorithms for manycore GPUs

GPUs and the Future of Parallel Computing

Survey of Polygonal Surface Simplification Algorithms

Scalable GPU graph traversal

Parallel Computing Experiences with CUDA