CORRELATION DETECTION IN TREES FOR PLANTED GRAPH ALIGNMENT

• 成果类型: Article
• 署名作者: Ganassali, Luca; Lelarge, Marc; Massoulie, Laurent
• 署名单位: Universite PSL; Ecole Normale Superieure (ENS); Inria
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/23-AAP2020
• 发表日期: 2024
• 页码: 2799-2843
• 关键词: recovery

摘要

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