A polynomial-time iterative algorithm for random graph matching with non-vanishing correlation

• URL: http://arxiv.org/abs/2306.00266v2
• Date: Wed, 6 Mar 2024 03:30:41 GMT
• Title: A polynomial-time iterative algorithm for random graph matching with non-vanishing correlation
• Authors: Jian Ding, Zhangsong Li
• Abstract summary: We propose an efficient algorithm for matching two correlated ErdHos--R'enyi graphs with $n$ whose edges are correlated through a latent correspondence. Our algorithm has running time and succeeds to recover the latent matching as long as the edge correlation is non-vanishing.
• Score: 12.869436542291144
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose an efficient algorithm for matching two correlated Erd\H{o}s--R\'enyi graphs with $n$ vertices whose edges are correlated through a latent vertex correspondence. When the edge density $q= n^{- \alpha+o(1)}$ for a constant $\alpha \in [0,1)$, we show that our algorithm has polynomial running time and succeeds to recover the latent matching as long as the edge correlation is non-vanishing. This is closely related to our previous work on a polynomial-time algorithm that matches two Gaussian Wigner matrices with non-vanishing correlation, and provides the first polynomial-time random graph matching algorithm (regardless of the regime of $q$) when the edge correlation is below the square root of the Otter's constant (which is $\approx 0.338$).

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