The problem of aligning Erd\"os-R\'enyi random graphs is a noisy, average-case version of the graph isomorphism problem, in which a pair of correlated random graphs is observed through a random permutation of their vertices. We study a polynomial time message-passing algorithm devised to solve the inference problem of partially recovering the hidden permutation, in the sparse regime with constant average degrees. We perform extensive numerical simulations to determine the range of parameters in which this algorithm achieves partial recovery. We also introduce a generalized ensemble of correlated random graphs with prescribed degree distributions, and extend the algorithm to this case.

翻译：将 Erd\" os- R\' enyi 随机图解对齐的问题是一个非常吵闹的、普通的图形形态问题,其中通过随机的脊椎变形观测到一对相关随机图。我们研究了一种多元时间信息传递算法,目的是用恒定平均度在稀疏的状态下解决部分恢复隐藏的变异的推论问题。我们进行了广泛的数字模拟,以确定该算法部分恢复的参数范围。我们还引入了带有规定度分布的通用相关随机图解,并将算法扩大到此案例。