[2306.00266] A polynomial-time iterative algorithm for random graph matching with non-vanishing correlation

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Summary:We suggest an environment friendly algorithm for matching two correlated Erdős–Rényi graphs with $n$ vertices whose edges are correlated by means of a latent vertex correspondence. When the sting density $q= n^{- alpha+o(1)}$ for a continuing $alpha in [0,1)$, 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 $approx 0.338$).

Submission history

From: Jian Ding [view email]
[v1]
Thu, 1 Jun 2023 00:58:50 UTC (174 KB)
[v2]
Wed, 6 Mar 2024 03:30:41 UTC (179 KB)



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