# 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} }

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

### A polynomial time iterative algorithm for matching Gaussian matrices with non-vanishing correlation

- Computer Science, MathematicsArXiv
- 2022

This work proposes an iterative matching algorithm, which succeeds in polynomial time as long as the correlation between the two Gaussian matrices does not vanish.

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