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arXiv · 2205.14650

Matching recovery threshold for correlated random graphs

Jian Ding·Hang Du
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Abstract

For two correlated graphs which are independently sub-sampled from a common Erdős-Rényi graph $\mathbf{G}(n, p)$, we wish to recover their \emph{latent} vertex matching from the observation of these two graphs \emph{without labels}. When $p = n^{-α+o(1)}$ for $α\in (0, 1]$, we establish a sharp information-theoretic threshold for whether it is possible to correctly match a positive fraction of vertices. Our result sharpens a constant factor in a recent work by Wu, Xu and Yu.

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Jian Ding, Hang Du. 2022-05-29. Matching recovery threshold for correlated random graphs. https://arxiv.org/abs/2205.14650

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