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

Abstract

We propose an efficient algorithm for matching two correlated Erdős--Rényi 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 $\approx 0.338$).

62 pages, 1 figure

Cited by in corpus (1)

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