第一眼:基于线性代数的三角形计数,没有矩阵乘法

Tze Meng Low, Varun Nagaraj Rao, Matthew Kay Fei Lee, Doru-Thom Popovici, F. Franchetti, Scott McMillan
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引用次数: 20

摘要

基于线性代数的精确三角形计数方法通常需要将稀疏矩阵乘法作为基本运算。处理相同问题的非线性代数方法通常假设图的邻接矩阵不可用。在本文中,我们证明了这两种方法可以统一为一种将数据格式与算法设计分离的方法。通过不将三角形计数算法转换为矩阵乘法,可以确定对每个三角形精确计数一次的不同算法。此外,通过选择适当的稀疏矩阵格式,我们证明了相同的算法等价于假设图的邻接矩阵不可用的紧前算法。我们表明,我们的方法产生的初始实现比参考实现快69到2000多倍。我们还表明,初始实现可以很容易地在共享内存系统上并行化。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
First look: Linear algebra-based triangle counting without matrix multiplication
Linear algebra-based approaches to exact triangle counting often require sparse matrix multiplication as a primitive operation. Non-linear algebra approaches to the same problem often assume that the adjacency matrix of the graph is not available. In this paper, we show that both approaches can be unified into a single approach that separates the data format from the algorithm design. By not casting the triangle counting algorithm into matrix multiplication, a different algorithm that counts each triangle exactly once can be identified. In addition, by choosing the appropriate sparse matrix format, we show that the same algorithm is equivalent to the compact-forward algorithm attained assuming that the adjacency matrix of the graph is not available. We show that our approach yields an initial implementation that is between 69 and more than 2000 times faster than the reference implementation. We also show that the initial implementation can be easily parallelized on shared memory systems.
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