High-performance Parallel Algorithms Research Articles

High-performance CGM-based parallel algorithms for minimum cost parenthesizing problem

High-performance CGM-based parallel algorithms for minimum cost parenthesizing problem

GeoGraph

In many applications of graph processing, the input data is often generated from an underlying geometric point data set. However, existing high-performance graph processing frameworks assume that the input data is given as a graph. Therefore, to use these frameworks, the user must write or use external programs based on computational geometry algorithms to convert their point data set to a graph, which requires more programming effort and can also lead to performance degradation. In this paper, we present our ongoing work on the Geo- Graph framework for shared-memory multicore machines, which seamlessly supports routines for parallel geometric graph construction and parallel graph processing within the same environment. GeoGraph supports graph construction based on k-nearest neighbors, Delaunay triangulation, and b-skeleton graphs. It can then pass these generated graphs to over 25 graph algorithms. GeoGraph contains highperformance parallel primitives and algorithms implemented in C++, and includes a Python interface. We present four examples of using GeoGraph, and some experimental results showing good parallel speedups and improvements over the Higra library. We conclude with a vision of future directions for research in bridging graph and geometric data processing.

High performance computing for global optimization problems

In the present work, we considered multiextremal optimization problems and a high-performance parallel algorithm for solving these ones. The investigation of the algorithm scalability has been carried out on the problem class, in which the computation costs of the function value evaluations can be varied at different iteration points. The algorithm proposed in the present work can utilize the CPUs (for solving more complex subproblems) as well as the GPUs (for solving the simple subproblems). We presented results of numerical experiments demonstrating the speedup when solving a series of multiextremal constrained problems.

HPC-NMF: A High-Performance Parallel Algorithm for Nonnegative Matrix Factorization

HPC-NMF: A High-Performance Parallel Algorithm for Nonnegative Matrix Factorization

A high-performance parallel algorithm for nonnegative matrix factorization

Non-negative matrix factorization (NMF) is the problem of determining two non-negative low rank factors W and H , for the given input matrix A , such that A ≈ WH . NMF is a useful tool for many applications in different domains such as topic modeling in text mining, background separation in video analysis, and community detection in social networks. Despite its popularity in the data mining community, there is a lack of efficient distributed algorithms to solve the problem for big data sets. We propose a high-performance distributed-memory parallel algorithm that computes the factorization by iteratively solving alternating non-negative least squares (NLS) subproblems for W and H . It maintains the data and factor matrices in memory (distributed across processors), uses MPI for interprocessor communication, and, in the dense case, provably minimizes communication costs (under mild assumptions). As opposed to previous implementations, our algorithm is also flexible: (1) it performs well for both dense and sparse matrices, and (2) it allows the user to choose any one of the multiple algorithms for solving the updates to low rank factors W and H within the alternating iterations. We demonstrate the scalability of our algorithm and compare it with baseline implementations, showing significant performance improvements.

New algorithm for simulation of 3D classical spin glasses under the influence of external electromagnetic fields

We study statistical properties of 3D classical spin-glass under the influence of external fields. It is proved that in the framework of the nearest-neighboring model 3D spin-glass problem at performing of Birkhoff’s ergodic hypothesis regarding to orientations of spins in the 3D space can be reduced to the problem of disordered 1D spatial spin-chains (SSC) ensemble where each spin-chain interacts with a random environment. The 1D SSC is defined as a periodic 1D lattice, where spins in nodes are randomly oriented in 3D space, in addition they all interact with each other randomly. For minimization of the Hamiltonian in an arbitrary node of the 1D lattice lattice, we obtained recurrent equations and corresponding Sylvester criterion, which allow to find energy local minimum. On the bases of these equations the high-performance parallel algorithm is developed which allows to calculate all statistical parameters of 3D spin glass, including distribution of a constant of spin-spin interaction, from the first principles of the classical mechanics.

Algorithms for Hessenberg-Triangular Reduction of Fiedler Linearization of Matrix Polynomials

Small- to medium-sized polynomial eigenvalue problems can be solved by linearizing the matrix polynomial and solving the resulting generalized eigenvalue problem using the QZ algorithm. The QZ algorithm, in turn, requires an initial reduction of a matrix pair to Hessenberg-triangular (HT) form. In this paper, we discuss the design and evaluation of high-performance parallel algorithms and software for HT reduction of a specific linearization of matrix polynomials of arbitrary degree. The proposed algorithm exploits the sparsity structure of the linearization to reduce the number of operations and improve the cache reuse compared to existing algorithms for unstructured inputs. Experiments on both a workstation and a high-performance computing system demonstrate that our structure-exploiting parallel implementation can outperform both the general LAPACK routine \tt DGGHRD and the prototype implementation \tt DGGHR3 of a general blocked algorithm.

High-performance parallel algorithms based on smoothed particles hydrodynamics for solving continuum mechanics problems

Continuum mechanics has a large number of important applications in physics, chemistry, engi� neering, and other fields. The deep level of modern

OpenMC: A state-of-the-art Monte Carlo code for research and development

This paper gives an overview of OpenMC, an open source Monte Carlo particle transport code recently developed at the Massachusetts Institute of Technology. OpenMC uses continuous-energy cross sections and a constructive solid geometry representation, enabling high-fidelity modeling of nuclear reactors and other systems. Modern, portable input/output file formats are used in OpenMC: XML for input, and HDF5 for output. High performance parallel algorithms in OpenMC have demonstrated near-linear scaling to over 100,000 processors on modern supercomputers. Other topics discussed in this paper include plotting, CMFD acceleration, variance reduction, eigenvalue calculations, and software development processes.

GACO: A GPU-based High Performance Parallel Multi-ant Colony Optimization Algorithm

As a population-based algorithm, Ant Colony Optimization (ACO) is intrinsically massively parallel, and therefore it is expected to be well-suited for implementation on GPUs (Graphics Processing Units). In this paper, we present a novel ant colony optimization algorithm (called GACO), which based on Compute Unified Device Architecture (CUDA) enabled GPU. In GACO algorithm, we utilize some novel optimizations, such as hybrid pheromone matrix update, dynamic nearest neighbor path construction, and multiple ant colony distribution, which result in a higher speedup and a better quality solutions compared to other peer of algorithms. GACO is tested by the Traveling Salesman Problem (TSP) benchmark, and the experimental results show a total speedup up to 40:1× and 35:7× over implementation of Ant Colony System (ACS) and Max-min Ant System (MMAS), respectively.

High-performance hybrid CPU and GPU parallel algorithm for digital volume correlation

We present a hybrid Message Passing Interface (MPI) and graphics processing unit (GPU)-based parallel digital volume correlation (DVC) algorithm for measuring three-dimensional (3D) displacement and strain fields inside a material undergoing motion or deformation. Our algorithm achieves resolution comparable to that achieved in two-dimensional (2D) digital image correlation (DIC), in time that is commensurate with the image acquisition time, in this case, using microcomputed tomography ([Formula: see text] CT) for scanning images. For DVC, the volume of data and number of correlation points both grow cubically with the linear dimensions of the image. We turn to parallel computing to gain sufficient processing power to scale to high resolution, and are able to achieve more than an order-of-magnitude increase in resolution compared with previous efforts that are not based on a parallel framework.

Parallel suffix array and least common prefix for the GPU

Suffix Array (SA) is a data structure formed by sorting the suffixes of a string into lexicographic order. SAs have been used in a variety of applications, most notably in pattern matching and Burrows-Wheeler Transform (BWT) based lossless data compression. SAs have also become the data structure of choice for many, if not all, string processing problems to which suffix tree methodology is applicable. Over the last two decades researchers have proposed many suffix array construction algorithm (SACAs). We do a systematic study of the main classes of SACAs with the intent of mapping them onto a data parallel architecture like the GPU. We conclude that skew algorithm [12], a linear time recursive algorithm, is the best candidate for GPUs as all its phases can be efficiently mapped to a data parallel hardware. Our OpenCL implementation of skew algorithm achieves a throughput of up to 25 MStrings/sec and a speedup of up to 34x and 5.8x over a single threaded CPU implementation using a discrete GPU and APU respectively. We also compare our OpenCL implementation against the fastest known CPU implementation based on induced copying and achieve a speedup of up to 3.7x. Using SA we construct BWT on GPU and achieve a speedup of 11x over the fastest known BWT on GPU. Suffix arrays are often augmented with the longest common prefix (LCP) information. We design a novel high-performance parallel algorithm for computing LCP on the GPU. Our GPU implementation of LCP achieves a speedup of up to 25x and 4.3x on discrete GPU and APU respectively.

A New Parallel Algorithm for Simulation of Spin-Glass Systems on Scales of Space-Time Periods of an External Field

We study the statistical properties of an ensemble of disordered 1D spatial spin-chains (SSCs) of certain length in the external field. On nodes of spin-chain lattice the recurrent equations and corresponding inequal-ity conditions are obtained for calculation of local minimum of a classical Hamiltonian. Using these equa-tions for simulation of a model of 1D spin-glass an original high-performance parallel algorithm is developed. Distributions of different parameters of unperturbed spin-glass are calculated. It is analytically proved and shown by numerical calculations that the distribution of the spin-spin interaction constant in the Heisenberg nearest-neighboring Hamiltonian model as opposed to the widely used Gauss-Edwards-Anderson distribu-tion satisfies the Levy alpha-stable distribution law which does not have variance. We have studied critical properties of spin-glass depending on the external field amplitude and have shown that even at weak external fields in the system strong frustrations arise. It is shown that frustrations have a fractal character, they are self-similar and do not disappear at decreasing of calculations area scale. After averaging over the fractal structures the mean values of polarizations of the spin-glass on the scales of external field's space-time peri-ods are obtained. Similarly, Edwards-Anderson’s ordering parameter depending on the external field ampli-tude is calculated. It is shown that the mean values of polarizations and the ordering parameter depending on the external field demonstrate phase transitions of first-order.

High-performance modeling acoustic and elastic waves using the parallel Dichotomy Algorithm

A high-performance parallel algorithm is proposed for modeling the propagation of acoustic and elastic waves in inhomogeneous media. An initial boundary-value problem is replaced by a series of boundary-value problems for a constant elliptic operator and different right-hand sides via the integral Laguerre transform. It is proposed to solve difference equations by the conjugate gradient method for acoustic equations and by the GMRES( k) method for modeling elastic waves. A preconditioning operator was the Laplace operator that is inverted using the variable separation method. The novelty of the proposed algorithm is using the Dichotomy Algorithm [26], which was designed for solving a series of tridiagonal systems of linear equations, in the context of the preconditioning operator inversion. Via considering analytical solutions, it is shown that modeling wave processes for long instants of time requires high-resolution meshes. The proposed parallel fine-mesh algorithm enabled to solve real application seismic problems in acceptable time and with high accuracy. By solving model problems, it is demonstrated that the considered parallel algorithm possesses high performance and efficiency over a wide range of the number of processors (from 2 to 8192).

High-Performance Domainwise Parallel Direct Solver for Large-Scale Structural Analysis

Large-scale structural analysis using a finite element method requires a high-performance and efficient parallel algorithm that is scalable in terms of both performance and storage. Most of the research for large-scale parallel structural analysis has focused on iterative solution methods because they are much easier to parallelize. In contrast, direct solution methods have generally been considered in adequate for large-scale finite element computations because of many difficulties and disadvantages for carrying out large-scale problems. However, direct solution methods are still generally preferred due to their ease of use and the numerical robustness that guarantees the solution to be obtained within an estimated time without failure. Therefore, for the general application of large-scale structural analysis to a wide range of problems, an efficient parallel direct solution method that has scalability comparable to that of iterative methods is proposed. A new parallel direct solver for large-scale finite element analysis, the domainwise multifrontal solver, is proposed by realizing domainwise parallelism for a direct solver. By the use of the proposed solver with our own structural analysis code, good scalability can be shown as a direct method and can solve the largest problem ever known to be solved by direct solvers.

Searching for Backbones—a high-performance parallel algorithm for solving combinatorial optimization problems

A highly efficient parallel algorithm called Searching for Backbones (SfB) is proposed: based on the finding, that many parts of a good configuration for a given optimization problem are the same in all other good solutions, SfB reduces the complexity of this problem by determining these “backbones” and eliminating them in order to get even better solutions in a very short time. Applications and results are presented for the Traveling Salesman Problem and the Vehicle Routing Problem.

Optimal control of adaptive building structures under blast loading

>Creation of a new generation of high-performance adaptive⧹smart structures with self-modification capability is advanced to resist dynamic loadings due to both nature such as wind and earthquake loadings and man such as blast and bomb loadings. The general computational models and high-performance parallel algorithms developed recently by the authors for optimal control of large structures are applied to multistorey building structures subjected to blast loadings. Both internal blast loading at different floor levels and external blast loading from outside the structure are considered. Results are presented for several regular and irregular moment-resisting steel space frame structures. It is demonstrated that the response of a building structure to blast loadings can be reduced substantially to a fraction of the response of the uncontrolled structure. © 1998 Elsevier Science Ltd. All rights reserved.

A High-Performance Parallel Algorithm to Search Depth-First Game Trees

A High-Performance Parallel Algorithm to Search Depth-First Game Trees