An evaluation of four reordering algorithms to reduce the computational cost of the Jacobi-preconditioned Conjugate Gradient Method using high-precision arithmetic

Oliveira, Sanderson L. Gonzaga de; Abreu, Alexandre A. A. M. de; Robaina, Diogo T.; Kischinhevsky, Mauricio

doi:10.1504/ijbidm.2017.10004158

Cited by 6 publications

(12 citation statements)

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“…Using a heuristic for matrix bandwidth reduction is an important choice to produce a sequence of graph (of the underlying matrix A) vertices with the spatial locality. Therefore, practitioners employ heuristics for bandwidth reduction to provide low processing costs for solving large sparse linear systems by iterative methods [16,17]. Bandwidth reduction is also employed in other fields, such as in the context of browsing hypertext [3], small world networks [21], visual analysis of data sets using visual similarity matrices [25], graph entropy rate minimization [4], symbolic model checking [1], mesh layout optimization [6] and the seriation problem [7].…”

Section: Introductionmentioning

confidence: 99%

“…Since the mid-1960s, practitioners have proposed heuristics for bandwidth reduction [5,16]. Previous publications [5,[16][17][18]20] have reviewed various heuristics and have indicated the most promising low-cost heuristics for bandwidth reduction so that they can be used in a preprocessing step when solving linear systems [20]. In this context, practical heuristics for bandwidth reduction compute at low cost and yield reasonable bandwidth results [16,17,20].…”

Section: Introductionmentioning

confidence: 99%

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Low-cost heuristics for matrix bandwidth reduction combined with a Hill-Climbing strategy

Oliveira

Silva

2021

RAIRO-Oper. Res.

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This paper studies heuristics for the bandwidth reduction of large-scale matrices in serial computations. Bandwidth optimization is a demanding subject for a large number of scientific and engineering applications. A heuristic for bandwidth reduction labels the rows and columns of a given sparse matrix. The algorithm arranges entries with a nonzero coefficient as close to the main diagonal as possible. This paper modifies an ant colony hyper-heuristic approach to generate expert-level heuristics for bandwidth reduction combined with a Hill-Climbing strategy when applied to matrices arising from specific application areas. Specifically, this paper uses low-cost state-of-the-art heuristics for bandwidth reduction in tandem with a Hill-Climbing procedure. The results yielded on a wide-ranging set of standard benchmark matrices showed that the proposed strategy outperformed low-cost state-of-the-art heuristics for bandwidth reduction when applied to matrices with symmetric sparsity patterns.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Low-cost heuristics for matrix bandwidth reduction combined with a Hill-Climbing strategy

Oliveira

Silva

2021

RAIRO-Oper. Res.

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“…Neste presente trabalho, comparamos resultados do método DRSA com o método Reverse Cuthill-McKee (RCM) [6] com vértices iniciais fornecidos pelo algoritmo de George-Liu [7,8]. Esse métodoé um dos mais conhecidos para redução de largura de banda de matrizes [1,3,10,11,12,18]. O método RCM-GL [8] fornece reduções de largura de banda razoáveis, a custo de execução extremamente baixo.…”

Section: Introductionunclassified

“…Nossos experimentos também avaliam as heurísticas de Koohestani e Poli (KP-band) [15] e a busca em largura com ordenação inversa (RBFS) [12] para numeração de vértices. Em publicações anteriores [11,10,12], foi verificado que esses três algoritmos fornecem resultados melhores que algoritmos baseados em meta-heurísticas, se o custo computacional (tempo de execução e ocupação de memória)é levado em consideração.…”

Section: Introductionunclassified

Um análise comparativa entre quatro algoritmos para reduções de largura de banda de matrizes

Oliveira¹,

Chagas²

2019

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics

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Resumo. Neste trabalho,é relatado um experimento computacional com o objetivo de comparar quatro algoritmos heurísticos que podem ser considerados, em diferentes situações, os principais métodos em redução de largura de banda de matrizes. Foi publicado, recentemente, o algoritmo Dual Representation Simulated Annealing para redução de largura de banda de matrizes. Os resultados desse algoritmo superaram os resultados de outro algoritmo, baseado na metaheurística Variable Neighborhood Search, considerada pelos autores como o método no estado da arte anterior no problema. Neste contexto, as heurísticas devem apresentar custo de execução muito baixo, pois são utilizadas para acelerar resolutores de sistemas de equações lineares. Entretanto, em geral, algoritmos baseados em meta-heurísticas são lentos e não são eficazes nesse problema de otimização combinatória, mesmo quando aplicados em instâncias pequenas. Neste trabalho, comparamos resultados do algoritmo Dual Representation Simulated Annealing com resultados do método Reverse Cuthill-McKee, uma variação desse método e uma variação da busca em largura, que foram consideradas, recentemente, as três heurísticas de baixo custo de execução mais promissoras no problema de redução de largura de banda, para diferentesáreas de aplicação. Baseados nos resultados de nossos experimentos, consideramos que essas três heurísticas de baixo custo de processamento superam o algoritmo Dual Representation Simulated Annealing, quando o tempo de execuçãoé uma variável considerada na comparação. Palavras-chave. Matrizes esparsas, algoritmos em grafos, redução de largura de banda, teoria dos grafos, renumeração de vértices.

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“…The George-Liu algorithm (GL) [10] is the state-of-the-practice method for providing pseudoperipheral (see definitions below) vertices to the Reverse Cuthill-McKee method. Thus, this matrix bandwidth method starting with a pseudoperipheral vertex given by the George-Liu algorithm [10] is one of the best-known and widely used heuristics for bandwidth reductions of matrices (see [3,4,9,12,14,16,17] and references therein). For instance, the method is available on MATLAB [9,12,22] and GNU Octave [8,9] as the function symrcm 1 , and on Boost C++ Library [20] 2 .…”

Section: Introductionmentioning

confidence: 99%

An Experimental Analysis of Three Pseudo-peripheral Vertex Finders in conjunction with the Reverse Cuthill-McKee Method for Bandwidth Reduction

Oliveira¹,

Abreu²

2019

Tend. Mat. Apl. Comput.

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The need to determine pseudoperipheral vertices arises from several graph-theoretical approaches for ordering sparse matrix equations. Results of two algorithms for finding such vertices, namely, the George-Liu and Kaveh-Bondarabady algorithms, are evaluated in this work along with a variant of the Kaveh-Bondarabady algorithm. Experiments among these three algorithms in conjunction with the Reverse Cuthill-McKee method suggest that the modified algorithm is a suitable alternative for reducing bandwidth of matrices that arise from specific application area, but it is dominated by the well-know George-Liu algorithm mainly when considering the computational times of the algorithms.

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An evaluation of four reordering algorithms to reduce the computational cost of the Jacobi-preconditioned Conjugate Gradient Method using high-precision arithmetic

Cited by 6 publications

References 19 publications

Low-cost heuristics for matrix bandwidth reduction combined with a Hill-Climbing strategy

Low-cost heuristics for matrix bandwidth reduction combined with a Hill-Climbing strategy

Um análise comparativa entre quatro algoritmos para reduções de largura de banda de matrizes

An Experimental Analysis of Three Pseudo-peripheral Vertex Finders in conjunction with the Reverse Cuthill-McKee Method for Bandwidth Reduction

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