RCM++:Reverse Cuthill-McKee ordering with Bi-Criteria Node Finder

arXiv - CS - Data Structures and Algorithms Pub Date : 2024-09-06 DOI:arxiv-2409.04171

JiaJun Hou, HongJie Liu, ShengXin Zhu

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Abstract

The Reverse Cuthill-McKee (RCM) algorithm is a graph-based method for reordering sparse matrices, renowned for its effectiveness in minimizing matrix bandwidth and profile. This reordering enhances the efficiency of matrix operations, making RCM pivotal among reordering algorithms. In the context of executing the RCM algorithm, it is often necessary to select a starting node from the graph representation of the matrix. This selection allows the execution of BFS (Breadth-First Search) to construct the level structure. The choice of this starting node significantly impacts the algorithm's performance, necessitating a heuristic approach to identify an optimal starting node, commonly referred to as the RCM starting node problem. Techniques such as the minimum degree method and George-Liu (GL) algorithm are popular solutions. This paper introduces a novel algorithm addressing the RCM starting node problem by considering both the eccentricity and the width of the node during the run. Integrating this algorithm with the RCM algorithm, we introduce RCM++. Experimental results demonstrate that RCM++ outperforms existing RCM methods in major software libraries, achieving higher quality results with comparable computation time. This advancement fosters the further application and development of the RCM algorithm.The code related to this research has been made available at https://github.com/SStan1/RCM\_PP.git.

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RCM++：利用双标准节点查找器进行反向 Cuthill-McKee 排序

Reverse Cuthill-McKee（RCM）算法是一种基于图的稀疏矩阵重排序方法，因其在最小化矩阵带宽和轮廓方面的有效性而闻名。这种重新排序提高了矩阵运算的效率，使 RCM 成为重新排序算法中的佼佼者。在执行 RCM 算法时，通常需要从矩阵的图表示中选择一个起始节点。这一选择允许执行 BFS（广度优先搜索）来构建层级结构。起始节点的选择会严重影响算法的性能，因此需要采用启发式方法来确定最佳起始节点，这通常被称为 RCM 起始节点问题。最小度法和乔治-刘（GL）算法等技术是常用的解决方案。本文介绍了一种解决 RCM 起始节点问题的新算法，它在运行过程中同时考虑了节点的偏心率和宽度。实验结果表明，RCM++ 优于主要软件库中的现有 RCM 方法，在计算时间相当的情况下获得了更高质量的结果。这一进步促进了 RCM 算法的进一步应用和发展。与本研究相关的代码已在 https://github.com/SStan1/RCM\_PP.git 上公布。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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arXiv - CS - Data Structures and Algorithms

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