The algorithmic phase transition of random graph alignment problem
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440_2025_1370_ReferencePDF.pdf
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Author(s)
Du, Hang
Gong, Shuyang
Huang, Rundong
Date Issued
March 26, 2025
Journal
Probability Theory and Related Fields
Publisher
Springer Berlin Heidelberg
Citation
Du, H., Gong, S. & Huang, R. The algorithmic phase transition of random graph alignment problem. Probab. Theory Relat. Fields 191, 1233–1288 (2025).
Version
Author's final manuscript
Abstract
We study the graph alignment problem over two independent Erdős–Rényi random graphs on n vertices, with edge density p falling into two regimes separated by the critical window around p c : = log n / n . Our result reveals an algorithmic phase transition for this random optimization problem: polynomial-time approximation schemes exist in the sparse regime, while statistical-computational gap emerges in the dense regime. Additionally, we establish a sharp transition on the performance of online algorithms for this problem when p is in the dense regime, resulting in a 8 / 9 multiplicative constant factor gap between achievable solutions and optimal solutions.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s00440-025-01370-z
