Matching recovery threshold for correlated random graphs

• URL: http://arxiv.org/abs/2205.14650v1
• Date: Sun, 29 May 2022 13:04:20 GMT
• Title: Matching recovery threshold for correlated random graphs
• Authors: Jian Ding, Hang Du
• Abstract summary: For two correlated graphs which are independently sub-sampled from a common ErdHos-R'enyi graph $mathbfG(n, p)$, we wish to recover their emphlatent matching from the observation of these two graphs emphwithout labels. Our result sharpens a constant factor in a recent work by Wu, Xu and Yu.
• Score: 9.12788494573002
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: For two correlated graphs which are independently sub-sampled from a common Erd\H{o}s-R\'enyi 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 $p = n^{-\alpha+o(1)}$ for $\alpha\in (0, 1]$, 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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