Parallel Implementation of the Gauss-Seidel Algorithm on &amp;lt;i&amp;gt;k&amp;lt;/i&amp;gt;-Ary &amp;lt;i&amp;gt;n&amp;lt;/i&amp;gt;-Cube Machine

Al-Towaiq, Mohammad H.

doi:10.4236/am.2013.41a028

Cited by 4 publications

(2 citation statements)

References 19 publications

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“…They stated that any fixed length Gauss‐Seidel schedule has an equivalent parallel execution which can be derived from a coloring of the dependency graph. In the following years, there have developed many parallel Gauss‐Seidel methods to process different linear systems that are abstracted from different applications . For instance, Koester et al came up with a parallel sparse Gauss‐Seidel solver with the potential for good relative speedup for the very sparse and irregular matrices encountered in the electrical power system application .…”

Section: Related Workmentioning

confidence: 99%

Improving parallel efficiency for asynchronous graph analytics using Gauss‐Seidel‐based matrix computation

Luo

Liu

2019

Concurrency and Computation

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Graph analytics is extensively used in big-data applications such as social networks, web analysis, bio-informatics, etc. Most graph processing frameworks adopt vertex-centric model due to its ease of use and programming. However, when dealing with asynchronous graph analytics, frameworks based on vertex programming perform inefficiently. The reason is that first, vertex programming must guarantee the sequential consistency, which means frequent use of locks or atomic operations, and second, the algorithms are parallelized in vertex level and latent parallelism of the algorithms cannot be exploited. To improve parallel efficiency of asynchronous graph processing, the Gauss-Seidel style algorithms in particular, this paper proposes a scheduling model using Gauss-Seidel-based matrix computation, which converts the vertex programming into two main matrix operations and then algorithms are parallelized by row and column vectors. Compared to vertex programming, our model parallelizes algorithms in a finer way to exploit more latent parallelism, while retains the ease-of-programming advantage of vertex programming. Instead of using locks to guarantee the sequential consistency, our model uses a hybrid synchronization policy to reduce serializability among threads and overheads of context switching. Furthermore, this model strengthens locality of the program. Experiment results show that our model outperforms vertex-centric asynchronous frameworks in both performance and scalability. Moreover, it even surpasses the matrix-based synchronous framework GraphMat with some non-Gauss-Seidel style algorithms. KEYWORDSasynchronous graph processing, Gauss-Seidel method, matrix computation INTRODUCTIONWith the advent of big data era, graph processing plays a vital role in various domains including social networks, 1,2 web analysis, 3,4 bio-informatics, 5 etc. To deal with these application requirements, many graph processing frameworks 6-15 have arisen in recent years, developing several programming models. The vertex-centric programming model, also called ''think like a vertex,'' is the most popular one due to its ease of programming.However, the execution efficiency of the graph analytics frameworks based on the vertex-centric programming model is not satisfied in some cases. For example, these frameworks perform inefficiently when dealing with asynchronous graph analytics, particularly, the Gauss-Seidel style algorithms, a class of algorithms that process graphs in Gauss-Seidel logic and are extensively used in social networks, machine learning, linear systems, etc. Typical Gauss-Seidel style algorithms include label propagation, coordinate descent, graph coloring, and so on, and they are inherently sequential and show poor parallelism. Some frameworks based on vertex-centric programming model support solving the Gauss-Seidel style problems. Thereinto, GraphLab, 9 for instance, is a famous one, which comes up with the round-robin scheduler with edge consistency model for the Gauss-Seidel style algorithms. Nevertheless, it is h...

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Section: Related Workmentioning

confidence: 99%

Improving parallel efficiency for asynchronous graph analytics using Gauss‐Seidel‐based matrix computation

Luo

Liu

2019

Concurrency and Computation

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“…It is well known that FD schemes are applied to solve systems of PDEs with many nodes on their structured domains [5]. The resulting algebraic systems are solved using iterative methods due to the fact that direct methods have disadvantages to calculate inverse matrices [6]. To reach higher accuracy and faster convergence rate, modifications have been made over iterative implicit methods, such as Jacobi, Gauss-Seidel and SOR, to have parallel algorithms, e.g.…”

Section: Introductionmentioning

confidence: 99%

A Parallel Implementation on CUDA for Solving 2D Poisson’s Equation

Clouthier-Lopez¹,

Barrón-Fernández²,

Salas-de-León³

2018

RCS

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A parallel iterative Finite Difference (FD) method for solving Poisson's equation on CUDA is implemented. The aim of this paper is to give a detail explanation about the parallel solution of a Partial Differential Equation (PDE). To examine the performance of the implemented iterative algorithm, a number of experiments were tested. The performance shows the benefit of using the implemented approach on GPU devices in terms of execution time.

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Continuous development of schemes for parallel computing of the electrostatics in biological systems: Implementation in DelPhi

Petukh

et al. 2013

J Comput Chem

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Due to the enormous importance of electrostatics in molecular biology, calculating the electrostatic potential and corresponding energies has become a standard computational approach for the study of biomolecules and nano-objects immersed in water and salt phase or other media. However, the electrostatics of large macromolecules and macromolecular complexes, including nano-objects, may not be obtainable via explicit methods and even the standard continuum electrostatics methods may not be applicable due to high computational time and memory requirements. Here, we report further development of the parallelization scheme reported in our previous work (J Comput Chem. 2012 Sep 15; 33(24):1960–6.) to include parallelization of the molecular surface and energy calculations components of the algorithm. The parallelization scheme utilizes different approaches such as space domain parallelization, algorithmic parallelization, multi-threading, and task scheduling, depending on the quantity being calculated. This allows for efficient use of the computing resources of the corresponding computer cluster. The parallelization scheme is implemented in the popular software DelPhi and results in speedup of several folds. As a demonstration of the efficiency and capability of this methodology, the electrostatic potential and electric field distributions are calculated for the bovine mitochondrial supercomplex illustrating their complex topology which cannot be obtained by modeling the supercomplex components alone.

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Parallel Implementation of the Gauss-Seidel Algorithm on <i>k</i>-Ary <i>n</i>-Cube Machine

Abstract: In this paper, we present parallel implementation of the Gauss-Seidel (GS) iterative algorithm for the solution of linear systems of equations on a k-ary n-cube parallel machine using Open MPI as a parallel programming environment. The proposed algorithm is of O(N

Cited by 4 publications

References 19 publications

Improving parallel efficiency for asynchronous graph analytics using Gauss‐Seidel‐based matrix computation

Improving parallel efficiency for asynchronous graph analytics using Gauss‐Seidel‐based matrix computation

A Parallel Implementation on CUDA for Solving 2D Poisson’s Equation

Continuous development of schemes for parallel computing of the electrostatics in biological systems: Implementation in DelPhi

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