Journal Articles The Annals of Applied Probability Year : 2024

Correlation detection in trees for planted graph alignment

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 MPAlign, a message-passing algorithm for graph alignment inspired by the tree correlation detection problem. We prove MPAlign 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. 1

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Dates and versions

hal-04893755 , version 1 (17-01-2025)

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Luca Ganassali, Marc Lelarge, Laurent Massoulié. Correlation detection in trees for planted graph alignment. The Annals of Applied Probability, 2024, 34 (3), ⟨10.1214/23-AAP2020⟩. ⟨hal-04893755⟩
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