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arxiv: 1711.06783 · v2 · pith:LHCNMOOXnew · submitted 2017-11-18 · 💻 cs.IT · cs.LG· math.IT

Exact alignment recovery for correlated ErdH{o}s-R\'enyi graphs

classification 💻 cs.IT cs.LGmath.IT
keywords vertexcorrespondencegraphscorrelatedenyiexactrecoveryalignment
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We consider the problem of perfectly recovering the vertex correspondence between two correlated Erd\H{o}s-R\'enyi (ER) graphs on the same vertex set. The correspondence between the vertices can be obscured by randomly permuting the vertex labels of one of the graphs. We determine the information-theoretic threshold for exact recovery, i.e. the conditions under which the entire vertex correspondence can be correctly recovered given unbounded computational resources.

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Cited by 4 Pith papers

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    The paper characterizes exact and partial recovery thresholds in the featured correlated Gaussian Wigner model and proposes the QPAlign quadratic programming algorithm with theoretical guarantees.

  2. The feasibility of multi-graph alignment: a Bayesian approach

    math.ST 2025-02 unverdicted novelty 7.0

    Establishes an all-or-nothing threshold for exact multi-graph alignment in the Gaussian model and a partial-alignment threshold in the sparse Erdős-Rényi model using a general Bayesian estimation framework over metric spaces.

  3. Spectral Graph Matching and Regularized Quadratic Relaxations I: The Gaussian Model

    stat.ML 2019-07 unverdicted novelty 7.0

    GRAMPA recovers exact vertex correspondence in the Gaussian Wigner model with high probability for σ = O(1/log n) via a regularized quadratic relaxation using all eigenvector pairs.

  4. The Umeyama algorithm for matching correlated Gaussian geometric models in the low-dimensional regime

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    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).