  Given two graphs, the graph matching problem is to align the two vertex sets
so as to minimize the number of adjacency disagreements between the two graphs.
The seeded graph matching problem is the graph matching problem when we are
first given a partial alignment that we are tasked with completing. In this
paper, we modify the state-of-the-art approximate graph matching algorithm
"FAQ" of Vogelstein et al. (2015) to make it a fast approximate seeded graph
matching algorithm, adapt its applicability to include graphs with differently
sized vertex sets, and extend the algorithm so as to provide, for each
individual vertex, a nomination list of likely matches. We demonstrate the
effectiveness of our algorithm via simulation and real data experiments;
indeed, knowledge of even a few seeds can be extremely effective when our
seeded graph matching algorithm is used to recover a naturally existing
alignment that is only partially observed.
