New Algorithm Achieves Robust Graph Matching Under Adversarial Perturbations
Researchers have developed an approximate message passing (AMP)-type algorithm that solves the random graph matching problem robustly, even when inputs are adversarially corrupted on a sublinear portion of vertices. The algorithm operates on correlated Gaussian Wigner matrix pairs and succeeds in polynomial time provided the inter-graph correlation is a non-vanishing constant and the adversarial perturbation affects at most o(1/(log n)^20) fraction of vertices. This is the first known efficient graph matching algorithm proven to withstand adversarial perturbations of near-linear size, advancing both theoretical computer science and practical applications in network de-anonymization and data integration.
A new study accepted by IEEE Transactions on Information Theory introduces an AMP-type iterative algorithm for the robust graph matching problem on dense graphs. The setting involves a pair of correlated Gaussian Wigner matrices (A, B) whose latent vertex correspondence must be recovered, even when the observed inputs are perturbed by adversarially chosen matrices E and F supported on an unknown ε n × ε n principal minor. The algorithm succeeds in polynomial time when the correlation ρ between the two graphs is a non-vanishing constant and ε = o(1/(log n)^20), meaning adversarial corruption can affect up to n^(1−o(1)) entries. A key algorithmic innovation is a time-dependent matrix multiplication step embedded within the AMP iteration, which simultaneously expands the feature dimension and cancels spurious correlations introduced by the adversary. The method builds on prior iterative graph matching algorithms and a spectral preprocessing procedure from recent literature. To the authors' knowledge, no prior efficient graph matching algorithm had been shown to be robust against adversarial perturbations of this scale. The work has implications for privacy, database alignment, and any domain requiring reliable identification of correspondences between noisy or tampered network data.
What's missing
The paper's robustness guarantee requires ε = o(1/(log n)^20), which is a very slowly growing but still restrictive bound; it remains an open question whether the algorithm or a variant can tolerate a constant fraction of adversarially corrupted vertices. The analysis is confined to the Gaussian Wigner model, and whether the results extend to sparse graphs or other random graph models (e.g., Erdős–Rényi) is not addressed. Empirical performance on real-world network datasets is not evaluated.
What different sources said
- arXiv cs.LGCenter
Robust Random Graph Matching in Dense Graphs via an Approximate Message Passing Type Algorithm
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