Impossibility of Partial Recovery in the Graph Alignment Problem
Abstract
Random graph alignment refers to recovering the underlying vertex correspondence between two random graphs with correlated edges. This can be viewed as an average-case and noisy version of the well-known graph isomorphism problem. For the correlated Erdös-Rényi model, we prove the first impossibility result for partial recovery in the sparse regime (with constant average degree). Our bound is tight in the noiseless case (the graph isomorphism problem) and we conjecture that it is still tight with noise. Our proof technique relies on a careful application of the probabilistic method to build automorphisms between tree components of a subcritical Erdös-Rényi graph.
Cite
Text
Ganassali et al. "Impossibility of Partial Recovery in the Graph Alignment Problem." Conference on Learning Theory, 2021.Markdown
[Ganassali et al. "Impossibility of Partial Recovery in the Graph Alignment Problem." Conference on Learning Theory, 2021.](https://mlanthology.org/colt/2021/ganassali2021colt-impossibility/)BibTeX
@inproceedings{ganassali2021colt-impossibility,
title = {{Impossibility of Partial Recovery in the Graph Alignment Problem}},
author = {Ganassali, Luca and Massoulie, Laurent and Lelarge, Marc},
booktitle = {Conference on Learning Theory},
year = {2021},
pages = {2080-2102},
volume = {134},
url = {https://mlanthology.org/colt/2021/ganassali2021colt-impossibility/}
}