Analytical Estimation of the Scalability of Iterative Numerical Algorithms on Distributed Memory Multiprocessors

Sokolinsky, Leonid B.

doi:10.1134/s1995080218040121

Cited by 15 publications

(10 citation statements)

References 22 publications

(26 reference statements)

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“…(we will explain the meaning of this constraint below). According to (15), inequalities a i , x b i and a l , x b l are similar if the following two conditions hold:…”

Section: Methods For Generating Random Lp Problemsmentioning

confidence: 99%

FRaGenLP: A Generator of Random Linear Programming Problems for Cluster Computing Systems

Sokolinsky,

Sokolinskaya

2021

Preprint

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The article presents and evaluates a scalable FRaGenLP algorithm for generating random linear programming problems of large dimension n on cluster computing systems. To ensure the consistency of the problem and the boundedness of the feasible region, the constraint system includes 2n + 1 standard inequalities, called support inequalities. New random inequalities are generated and added to the system in a manner that ensures the consistency of the constraints. Furthermore, the algorithm uses two likeness metrics to prevent the addition of a new random inequality that is similar to one already present in the constraint system. The algorithm also rejects random inequalities that cannot affect the solution of the linear programming problem bounded by the support inequalities. The parallel implementation of the FRaGenLP algorithm is performed in C++ through the parallel BSF-skeleton, which encapsulates all aspects related to the MPI-based parallelization of the program. We provide the results of large-scale computational experiments on a cluster computing system to study the scalability of the FRaGenLP algorithm.

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“…(we will explain the meaning of this constraint below). According to (15), inequalities a i , x b i and a l , x b l are similar if the following two conditions hold:…”

Section: Methods For Generating Random Lp Problemsmentioning

confidence: 99%

FRaGenLP: A Generator of Random Linear Programming Problems for Cluster Computing Systems

Sokolinsky,

Sokolinskaya

2021

Preprint

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“…The idea of the parallel computation model BSF (Bulk Synchronous Farm) was originally proposed in [9]. In this section, we present a brief description of an extension of the original model.…”

Section: Bsf Parallel Computation Modelmentioning

confidence: 99%

Scalability Evaluation of Iterative Algorithms Used for Supercomputer Simulation of Physical processes

Ezhova

Sokolinsky

2018

2018 Global Smart Industry Conference (GloSIC)

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The paper is devoted to the development of a methodology for evaluating the scalability of compute-intensive iterative algorithms used in simulating complex physical processes on supercomputer systems. The proposed methodology is based on the BSF (Bulk Synchronous Farm) parallel computation model, which makes it possible to predict the upper scalability bound of an iterative algorithm in early phases of its design. The BSF model assumes the representation of the algorithm in the form of operations on lists using high-order functions. Two classes of representations are considered: BSF-M (Map BSF) and BSF-MR (Map-Reduce BSF). The proposed methodology is described by the example of the solution of the system of linear equations by the Jacobi method. For the Jacobi method, two iterative algorithms are constructed: Jacobi-M based on the BSF-M representation and Jacobi-MR based on the BSF-MR representation. Analytical estimations of the speedup, parallel efficiency and upper scalability bound are constructed for these algorithms using the BSF cost metrics on multiprocessor computing systems with distributed memory. An information about the implementation of these algorithms in C++ language using the BSF program skeleton and MPI parallel programming library are given. The results of large-scale computational experiments performed on a cluster computing system are demonstrated. Based on the experimental results, an analysis of the adequacy of estimations obtained analytically by using the cost metrics of the BSF model is made.

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“…In that way, we get the following values for the cost parameters of the BSF model [21] in the case of the Cimmino algorithm:…”

Section: Analytical Evaluation Of Scalabilitymentioning

confidence: 99%

“…To determine the upper bound for the scalability of the Cimmino algorithm in accordance with the procedure described in [21], let us deduce the derivative a (K) and solve the equation…”

Section: Analytical Evaluation Of Scalabilitymentioning

confidence: 99%

“…To create a good parallel computation model, the designer must restrict the set of target multiprocessor architectures and class of algorithms. In paper [21], the parallel computation model BSF (Bulk Synchronous Farm) intended for cluster computing systems and iterative algorithms was proposed. The BSF model makes it possible to predict the upper scalability bound of an iterative algorithm with great accuracy before coding.…”

Section: Introductionmentioning

confidence: 99%

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Scalability Evaluation of Cimmino Algorithm for Solving Linear Inequality Systems on Multiprocessors with Distributed Memory

Sokolinsky

Sokolinskaya

2018

JSFI

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The paper is devoted to a scalability study of Cimmino algorithm for linear inequality systems. This algorithm belongs to the class of iterative projection algorithms. For the analytical analysis of the scalability, the BSF (Bulk Synchronous Farm) parallel computation model is used. An implementation of the Cimmino algorithm in the form of operations on lists using higher-order functions Map and Reduce is presented. An analytical estimation of the upper scalability bound of the algorithm for cluster computing systems is derived. An information about the implementation of Cimmino algorithm on lists in C++ language using the BSF program skeleton and MPI parallel programming library is given. The results of large-scale computational experiments performed on a cluster computing system are demonstrated. A conclusion about the adequacy of the analytical estimations by comparing them with the results of computational experiments is made.

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Analytical Estimation of the Scalability of Iterative Numerical Algorithms on Distributed Memory Multiprocessors

Cited by 15 publications

References 22 publications

FRaGenLP: A Generator of Random Linear Programming Problems for Cluster Computing Systems

FRaGenLP: A Generator of Random Linear Programming Problems for Cluster Computing Systems

Scalability Evaluation of Iterative Algorithms Used for Supercomputer Simulation of Physical processes

Scalability Evaluation of Cimmino Algorithm for Solving Linear Inequality Systems on Multiprocessors with Distributed Memory

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