Correcting the Output of Approximate Graph Matching Algorithms

Abstract

Approximate graph matching refers to the problem of finding the best correspondence between the node labels of two correlated graphs. The problem has been applied to a number of domains, including social network de-anonymization. Recently, a number of algorithms have been proposed for seeded graph matching, which uses a few seed matches between two graphs to determine the remaining correspondence. We adapt the ideas from seeded algorithms to develop a graph matching correction algorithm, which takes a partially correct correspondence as input and returns an improved correspondence. We show that this algorithm can correct all errors in graph matching for stochastic block model graphs with high probability. Finally, we apply our algorithm as a post-processing step for other approximate graph matching algorithms to significantly improve the performance of state-of-the-art algorithms for seedless graph matching.