We establish thresholds for the feasibility of random multi-graph alignment in two models. In the Gaussian model, we demonstrate an "all-or-nothing" phenomenon: above a critical threshold, exact alignment is achievable with high probability, while below it, even partial alignment is statistically impossible. In the sparse Erdős-Rényi model, we rigorously identify a threshold below which no meaningful partial alignment is possible and conjecture that above this threshold, partial alignment can be achieved. To prove these results, we develop a general Bayesian estimation framework over metric spaces, which provides insight into a broader class of high-dimensional statistical problems.
View on arXiv@article{vassaux2025_2502.17142,
title={ The feasibility of multi-graph alignment: a Bayesian approach },
author={ Louis Vassaux and Laurent Massoulié },
journal={arXiv preprint arXiv:2502.17142},
year={ 2025 }
}