Motivated by the problem of matching vertices in two correlated Erdős-Rényi graphs, we study the problem of matching two correlated Gaussian Wigner matrices. We propose an iterative matching algorithm, which succeeds in polynomial time as long as the correlation between the two Gaussian matrices does not vanish. Our result is the first polynomial time algorithm that solves a graph matching type of problem when the correlation is an arbitrarily small constant.

中文翻译：

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非零相关高斯矩阵匹配的多项式时间迭代算法

受两个相关 Erdős-Rényi 图中顶点匹配问题的启发，我们研究了匹配两个相关高斯维格纳矩阵的问题。我们提出了一种迭代匹配算法，只要两个高斯矩阵之间的相关性不消失，该算法就会在多项式时间内成功。我们的结果是第一个多项式时间算法，当相关性是任意小的常数时，它可以解决图匹配类型的问题。