# Random graph matching at Otter's threshold via counting chandeliers

@article{Mao2022RandomGM,
title={Random graph matching at Otter's threshold via counting chandeliers},
author={Cheng Mao and Yihong Wu and Jiaming Xu and Sophie H. Yu},
journal={ArXiv},
year={2022},
volume={abs/2209.12313}
}
• Published 25 September 2022
• Computer Science
• ArXiv
We propose an efficient algorithm for graph matching based on similarity scores constructed from counting a certain family of weighted trees rooted at each vertex. For two Erdős–Rényi graphs G(n, q) whose edges are correlated through a latent vertex correspondence, we show that this algorithm correctly matches all but a vanishing fraction of the vertices with high probability, provided that nq →∞ and the edge correlation coefficient ρ satisfies ρ > α ≈ 0.338, where α is Otter’s tree-counting…
2 Citations

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