A convex-concave relaxation procedure based subgraph matching algorithm

Based on the convex-concave relaxation procedure (CCRP), the (extended) path following algorithms were recently proposed to approximately solve the equal-sized graph matching problem, and exhibited a state-of-the-art performance (Zaslavskiy et al., 2009; Liu et al., 2012). However, they cannot be used for subgraph matching since either their convex or concave relaxation becomes no longer applicable. In this paper we extend the CCRP to tackle subgraph matching, by proposing a convex as well as a concave relaxation of the problem. Since in the context of CCRP, the convex relaxation can be viewed as an initialization of a concave programming, we introduce two other initializations for comparison. Meanwhile, the graduated assignment algorithm is also introduced in the experimental comparisons, which witness the validity of the proposed algorithm.