匹配非相关性高斯矩阵的多项式时间迭代算法

IF 2.5 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS Foundations of Computational Mathematics Pub Date : 2024-07-22 DOI:10.1007/s10208-024-09662-x

Jian Ding, Zhangsong Li

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引用次数: 0

摘要

受两个相关厄尔多斯-雷尼图中顶点匹配问题的启发，我们研究了两个相关高斯维格纳矩阵的匹配问题。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，该算法就能在多项式时间内取得成功。我们的成果是第一个在相关性为任意小常数时解决图匹配类型问题的多项式时间算法。

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A Polynomial Time Iterative Algorithm for Matching Gaussian Matrices with Non-vanishing Correlation

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.

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来源期刊

Foundations of Computational Mathematics 数学-计算机：理论方法

CiteScore

6.90

自引率

3.30%

发文量

审稿时长

>12 weeks

期刊介绍： Foundations of Computational Mathematics (FoCM) will publish research and survey papers of the highest quality which further the understanding of the connections between mathematics and computation. The journal aims to promote the exploration of all fundamental issues underlying the creative tension among mathematics, computer science and application areas unencumbered by any external criteria such as the pressure for applications. The journal will thus serve an increasingly important and applicable area of mathematics. The journal hopes to further the understanding of the deep relationships between mathematical theory: analysis, topology, geometry and algebra, and the computational processes as they are evolving in tandem with the modern computer. With its distinguished editorial board selecting papers of the highest quality and interest from the international community, FoCM hopes to influence both mathematics and computation. Relevance to applications will not constitute a requirement for the publication of articles. The journal does not accept code for review however authors who have code/data related to the submission should include a weblink to the repository where the data/code is stored.