  This thesis studies the graph alignment problem, the noisy version of the
graph isomorphism problem, which aims to find a matching between the nodes of
two graphs which preserves most of the edges. Focusing on the planted version
where the graphs are random, we are interested in understanding the fundamental
information-theoretical limits for this problem, as well as designing and
analyzing algorithms that are able to recover the underlying alignment in the
data. For these algorithms, we give some high probability guarantees on the
regime in which they succeed or fail.
