  Graph matching, also known as network alignment, refers to finding a
bijection between the vertex sets of two given graphs so as to maximally align
their edges. This fundamental computational problem arises frequently in
multiple fields such as computer vision and biology. Recently, there has been a
plethora of work studying efficient algorithms for graph matching under
probabilistic models. In this work, we propose a new algorithm for graph
matching and show that, for two Erd\H{o}s-R\'enyi graphs with edge correlation
$1-\alpha$, our algorithm recovers the underlying matching with high
probability when $\alpha \le 1 / (\log \log n)^C$, where $n$ is the number of
vertices in each graph and $C$ denotes a positive universal constant. This
improves the condition $\alpha \le 1 / (\log n)^C$ achieved in previous work.
