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

Autor:	Ding, Jian, Li, Zhangsong
Rok vydání:	2023
Předmět:	Computer Science - Data Structures and Algorithms Mathematics - Probability Mathematics - Statistics Theory Statistics - Machine Learning 68Q87 90C35
Druh dokumentu:	Working Paper
Popis:	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 $\approx 0.338$). Comment: 62 pages, 1 figure
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2306.00266 Zobrazit plný text záznamu View this record from Arxiv