用于植入图对齐的树中相关性检测
Correlation detection in trees for planted graph alignment
AI总结：
本文通过树相关性检测问题研究稀疏随机图对齐，提出MPAlign算法并证明其在树检测可行时可在多项式时间内完成部分对齐，同时猜想树检测不可能时图对齐在多项式时间内不可行，从而揭示图对齐的困难相。
摘要：
受相关稀疏随机图对齐问题的启发，我们引入了一个假设检验问题：判断两棵随机树是否相关。我们得到了该检验不可能或可行的充分条件。我们提出了MPAlign，这是一种受树相关性检测问题启发的用于图对齐的消息传递算法。我们证明，只要树检测是可行的，MPAlign就能在多项式时间内实现部分对齐。因此，我们对树检测的分析揭示了稀疏随机图部分对齐在多项式时间内可行的新的参数范围。我们随后猜想，当相关的树检测问题不可能时，图对齐在多项式时间内不可行。如果该猜想成立，那么它与我们关于树检测不可能性的充分条件一起，将意味着图对齐存在一个困难相，即一个参数范围，在该范围内，即使已知对齐在非多项式时间内可行，也无法在多项式时间内完成对齐。
英文摘要：
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 obtain sufficient conditions under which this testing 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. We then conjecture that graph alignment is not feasible in polynomial time when the associated tree detection problem is impossible. If true, this conjecture together with our sufficient conditions on tree detection impossibility would imply the existence of a hard phase for graph alignment, i.e. a parameter range where alignment cannot be done in polynomial time even though it is known to be feasible in non-polynomial time.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
