text: 60,155,1481151491243139076,883039700,Lenka Zdeborova,"I studied many inference problems on random graphs in the past, but the graph alignment is challenging: <LINK> We still do not know what are the constants for optimal behavior nor algorithms. A lot of work to do still here. @egavves Yes, this size is the parameter d, the influence is discussed in the paper.",https://arxiv.org/abs/2112.13079,"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. ","Aligning random graphs with a sub-tree similarity message-passing