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

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 nontrivial diameter. We present a BFS parallelization focused on fine-grained task management constructed from efficient prefix sum computations that achieves an asymptotically optimal O(|V| + |E|) gd 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 on both CPU and GPU platforms.

/pdf/high-performance-and-scalable-gpu-graph-traversal-k0liradfbb.pdf

High-Performance and Scalable GPU Graph Traversal

While many effective automatic surface simplification algorithms have been developed, they often produce poor approximations when a model is simplified to a very low level of detail. Furthermore, previous algorithms are not sensitive to semantic or high-level meanings of models. In this paper, we present a user-guided approach for mesh simpli cation that aims to overcome such limitations. Our proposed method allows users to selectively control the relative importance of different surface regions and preserve various features through the imposition of geometric constraints. Using our system, users can produce perceptually improved approximations with very little effort.

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User-guided simplification

We propose a new algorithm for constructing finite-element meshes suitable for spacetime discontinuous Galerkin solutions of linear hyperbolic PDEs. Given a triangular mesh of some planar domain Ω and a target time value T, our method constructs a tetrahedral mesh of the spacetime domain Ω X [0,T] in constant running time per tetrahedron in R3 using an advancing front method. Elements are added to the evolving mesh in small patches by moving a vertex of the front forward in time. Spacetime discontinuous Galerkin methods allow the numerical solution within each patch to be computed as soon as the patch is created. Our algorithm employs new mechanisms for adaptively coarsening and refining the front in response to a posteriori error estimates returned by the numerical code. A change in the front induces a corresponding refinement or coarsening of future elements in the spacetime mesh. Our algorithm adapts the duration of each element to the local quality, feature size, and degree of refinement of the underlying space mesh. We directly exploit the ability of discontinuous Galerkin methods to accommodate discontinuities in the solution fields across element boundaries.

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Spacetime meshing with adaptive refinement and coarsening

Modern enterprise applications represent an emergent application arena that requires the processing of queries and computations over massive amounts of data. Large-scale, multi-GPU cluster systems potentially present a vehicle for major improvements in throughput and consequently overall performance. However, throughput improvement using GPUs is challenged by the distinctive memory and computational characteristics of Relational Algebra (RA) operators that are central to queries for answering business questions.This paper introduces the design, implementation, and evaluation of Red Fox, a compiler and runtime infrastructure for executing relational queries on GPUs. Red Fox is comprised of i) a language front-end for LogiQL which is a commercial query language, ii) an RA to GPU compiler, iii) optimized GPU implementation of RA operators, and iv) a supporting runtime. We report the performance on the full set of industry standard TPC-H queries on a single node GPU. Compared with a commercial LogiQL system implementation optimized for a state of art CPU machine, Red Fox on average is 6.48x faster including PCIe transfer time. We point out key bottlenecks, propose potential solutions, and analyze the GPU implementation of these queries. To the best of our knowledge, this is the first reported end-to-end compilation and execution infrastructure that supports the full set of TPC-H queries on commodity GPUs.

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Red Fox: An Execution Environment for Relational Query Processing on GPUs

The advent of multicore CPUs and manycore GPUs means that mainstream processor chips are now parallel systems. Furthermore, their parallelism continues to scale with Moore's law. The challenge is to develop mainstream application software that transparently scales its parallelism to leverage the increasing number of processor cores, much as 3D graphics applications transparently scale their parallelism to manycore GPUs with widely varying numbers of cores.

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Michael Garland

Papers

High-Performance and Scalable GPU Graph Traversal

User-guided simplification

Spacetime meshing with adaptive refinement and coarsening

Red Fox: An Execution Environment for Relational Query Processing on GPUs

Scalable parallel programming