Graph alignment is a generic algorithmic problem with many applications. In this work we consider alignment of sparse random graphs generated from the correlated Erdös-Rényi distribution. We introduce the Neighborhood Tree Matching Algorithm which provably returns -- in polynomial time -- a positive fraction of correctly matched vertices, and a vanishing fraction of mismatches. This result holds in a challenging regime of graphs with average degree in O(1) and correlation parameter bounded away from 1. As a byproduct of the analysis we introduce a matching metric between trees and characterize it for several models of correlated random trees. These results may be of independent interest, yielding for instance efficient tests for determining whether two random trees are correlated or independent. If time allows we shall also describe recent results giving information-theoretic upper bounds on the best possible partial alignment achievable by any algorithm, polynomial-time or not. This is based on joint works with Luca Ganassali https://arxiv.org/abs/2002.01258 and Marc Lelarge https://arxiv.org/pdf/2102.02685.pdf .
Bio: Laurent Massoulié is research director at Inria, head of the Microsoft Research – Inria Joint Centre, and professor at the Applied Maths Centre of Ecole Polytechnique. His research interests are in machine learning, probabilistic modelling and algorithms for networks. He has held research scientist positions at: France Telecom, Microsoft Research, Thomson-Technicolor, where he headed the Paris Research Lab. He obtained best paper awards at IEEE INFOCOM 1999, ACM SIGMETRICS 2005, ACM CoNEXT 2007, NeurIPS 2018, was elected "Technicolor Fellow" in 2011, received the "Grand Prix Scientifique" of the Del Duca Foundation delivered by the French Academy of Science in 2017, and is a Fellow of the “Prairie” Institute.