Abstract
Motivated by alignment of correlated sparse random graphs, we introduce a hypothesis testing problem of deciding whether or not two random trees are correlated. We study the likelihood ratio test and obtain sufficient conditions under which this task is impossible or feasible. We propose , a message-passing algorithm for graph alignment inspired by the tree correlation detection problem. We prove to succeed in polynomial time at partial alignment whenever tree detection is feasible. As a result our analysis of tree detection reveals new ranges of parameters for which partial alignment of sparse random graphs is feasible in polynomial time.11
Funding Statement
This work was partially supported by the French government under management of Agence Nationale de la Recherche as part of the “Investissements d’avenir” program, reference ANR19-P3IA-0001 (PRAIRIE 3IA Institute).
Acknowledgments
The authors would like to thank Guilhem Semerjian for helpful discussions, and Jakob Maier for feedback on some of the proofs.
Citation
Luca Ganassali. Marc Lelarge. Laurent Massoulié. "Correlation detection in trees for planted graph alignment." Ann. Appl. Probab. 34 (3) 2799 - 2843, June 2024. https://doi.org/10.1214/23-AAP2020
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