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A Polynomial-time Iterative Algorithm for Random Graph Matching with Non-vanishing Correlation by Ding, Jian; Li, Zhangsong is a scholarly article available to read on EtoBox.

What is A Polynomial-time Iterative Algorithm for Random Graph Matching with Non-vanishing Correlation about?

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 $\approx 0.338$).

Author

Ding, Jian; Li, Zhangsong

Published

2023

Language

EN