Proves detection of RGG vs. ER is impossible for d ≫ (n h(p))^3 and d ≥ (1+ε)n, resolving the detection threshold conjecture in the regime p ≳ n^{-2/3}/log n.
arXiv preprint arXiv:2209.13723 , year=
2 Pith papers cite this work. Polarity classification is still indexing.
2
Pith papers citing it
verdicts
UNVERDICTED 2representative citing papers
Umeyama algorithm achieves exact recovery of latent permutation π* in correlated Gaussian geometric models for σ = o(d^{-3}n^{-2/d}) and almost exact for σ = o(d^{-3}n^{-1/d}) when d = O(log n).
citing papers explorer
-
Resolution of the Detection Threshold Conjecture for Random Geometric Graphs in the $d>n$ Regime
Proves detection of RGG vs. ER is impossible for d ≫ (n h(p))^3 and d ≥ (1+ε)n, resolving the detection threshold conjecture in the regime p ≳ n^{-2/3}/log n.
-
The Umeyama algorithm for matching correlated Gaussian geometric models in the low-dimensional regime
Umeyama algorithm achieves exact recovery of latent permutation π* in correlated Gaussian geometric models for σ = o(d^{-3}n^{-2/d}) and almost exact for σ = o(d^{-3}n^{-1/d}) when d = O(log n).