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

Finding the shortest paths from a single source to all other vertices is a fundamental method used in a variety of higher-level graph algorithms. We present three parallel friendly and work-efficient methods to solve this Single-Source Shortest Paths (SSSP) problem: Work front Sweep, Near-Far and Bucketing. These methods choose different approaches to balance the trade off between saving work and organizational overhead. In practice, all of these methods do much less work than traditional Bellman-Ford methods, while adding only a modest amount of extra work over serial methods. These methods are designed to have a sufficient parallel workload to fill modern massively-parallel machines, and select reorganizational schemes that map well to these architectures. We show that in general our Near-Far method has the highest performance on modern GPUs, outperforming other parallel methods. We also explore a variety of parallel load-balanced graph traversal strategies and apply them towards our SSSP solver. Our work-saving methods always outperform a traditional GPU Bellman-Ford implementation, achieving rates up to 14x higher on low-degree graphs and 340x higher on scale free graphs. We also see significant speedups (20-60x) when compared against a serial implementation on graphs with adequately high degree.

/pdf/work-efficient-parallel-gpu-methods-for-single-source-7p4imywo8d.pdf

Work-Efficient Parallel GPU Methods for Single-Source Shortest Paths

For workloads with abundant parallelism, GPUs deliver higher peak computational throughput than latency-oriented CPUs.

Understanding throughput-oriented architectures

Three dimensional scenes are typically modeled using a single, fixed resolution model of each geometric object. Renderings of such a model are often either slow or crude, however: slow for distant objects, where the chosen detail level is excessive, and crude for nearby objects, where the detail level is insufficient. What is needed is a multiresolution model that represents objects at multiple levels of detail. With a multiresolution model, a rendering program can choose the level of detail appropriate for the object’s screen size so that less time is wasted drawing insignificant detail. The principal challenge is the development of algorithms that take a detailed model as input and automatically simplify it, while preserving appearance. Multiresolution techniques can be used to speed many applications, including real time rendering for architectural and terrain simulators, and slower, higher quality rendering for entertainment and radiosity. This paper surveys existing multiresolution modeling techniques and speculates about what might be possible in the future.

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Multiresolution Modeling for Fast Rendering

Scan and segmented scan algorithms are crucial building blocks for a great many data-parallel algorithms. Segmented scan and related primitives also provide the necessary support for the attening transform, which allows for nested data-parallel programs to be compiled into at data-parallel languages. In this paper, we describe the design of ecient scan and segmented scan parallel primitives in CUDA for execution on GPUs. Our algorithms are designed using a divide-and-conquer approach that builds all scan primitives on top of a set of primitive intra-warp scan routines. We demonstrate that this design methodology results in routines that are simple, highly ecient, and free of irregular access patterns that lead to memory bank conicts. These algorithms form the basis for current and upcoming releases of the widely used CUDPP library.

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Efficient Parallel Scan Algorithms for GPUs

The growing availability of massive polygonal models, and the inability of most existing visualization tools to work with such data, has created a pressing need for memory-efficient methods capable of simplifying very large meshes. In this paper, we present a method for performing adaptive simplification of polygonal meshes that are too large to fit in-core. Our algorithm performs two passes over an input mesh. In the first pass, the model is quantized using a uniform grid, and surface information is accumulated in the form of quadrics and dual quadrics. This sampling is then used to construct a BSP-tree in which the partitioning planes are determined by the dual quadrics. In the final pass, the original vertices are clustered using the BSP-tree, yielding an adaptive approximation of the original mesh. The BSP-tree describes a natural simplification hierarchy, making it possible to generate a progressive transmission and construct level-of-detail representations. In this way, the algorithm provides some of the features associated with more expensive edge contraction methods while maintaining greater computational efficiency. In addition to performing adaptive simplification, our algorithm exhibits output-sensitive memory requirements and allows fine control over the size of the simplified mesh.

Michael Garland

Papers

Work-Efficient Parallel GPU Methods for Single-Source Shortest Paths

Understanding throughput-oriented architectures

Multiresolution Modeling for Fast Rendering

Efficient Parallel Scan Algorithms for GPUs

Efficient adaptive simplification of massive meshes