Seeded Graph Matching

TL;DR

This paper introduces a fast approximate seeded graph matching algorithm that leverages partial alignments to improve matching accuracy, adaptable to graphs of different sizes, and providing vertex match nominations.

Contribution

It modifies the FAQ algorithm for seeded graph matching, making it faster, adaptable to size differences, and capable of generating individual vertex match lists.

Findings

Effective with few seeds in recovering alignments

Demonstrated success on simulated and real data

Improves matching speed and accuracy

Abstract

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.