diGRASS: Directed Graph Spectral Sparsification via Spectrum-Preserving Symmetrization

IF 4 3区计算机科学 Q1 COMPUTER SCIENCE, INFORMATION SYSTEMS ACM Transactions on Knowledge Discovery from Data Pub Date : 2024-01-04 DOI:10.1145/3639568

Ying Zhang, Zhiqiang Zhao, Zhuo Feng

引用次数: 0

Abstract

Recent spectral graph sparsification research aims to construct ultra-sparse subgraphs for preserving the original graph spectral (structural) properties, such as the first few Laplacian eigenvalues and eigenvectors, which has led to the development of a variety of nearly-linear time numerical and graph algorithms. However, there is very limited progress for spectral sparsification of directed graphs. In this work, we prove the existence of nearly-linear-sized spectral sparsifiers for directed graphs under certain conditions. Furthermore, we introduce a practically-efficient spectral algorithm (diGRASS) for sparsifying real-world, large-scale directed graphs leveraging spectral matrix perturbation analysis. The proposed method has been evaluated using a variety of directed graphs obtained from real-world applications, showing promising results for solving directed graph Laplacians, spectral partitioning of directed graphs, and approximately computing (personalized) PageRank vectors.

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diGRASS：通过保留频谱的对称化实现有向图谱稀疏化

最近的图谱稀疏化研究旨在构建超稀疏子图，以保留原始图谱（结构）特性，如前几个拉普拉奇特征值和特征向量，这导致了各种近线性时间数值和图算法的发展。然而，有向图的谱稀疏化研究进展非常有限。在这项工作中，我们证明了在特定条件下，有向图存在近线性大小的谱稀疏化器。此外，我们还引入了一种实用高效的光谱算法（diGRASS），利用光谱矩阵扰动分析对现实世界中的大规模有向图进行稀疏化处理。我们使用从实际应用中获取的各种有向图对所提出的方法进行了评估，结果表明该方法在求解有向图拉普拉斯、有向图谱分区以及近似计算（个性化）PageRank 向量等方面具有良好的效果。

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来源期刊

ACM Transactions on Knowledge Discovery from Data COMPUTER SCIENCE, INFORMATION SYSTEMS-COMPUTER SCIENCE, SOFTWARE ENGINEERING

CiteScore

6.70

自引率

5.60%

发文量

172

审稿时长

3 months

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