Efficient Suboptimal Graph Isomorphism

In the field of structural pattern recognition, graphs provide us with a common and powerful way to represent objects. Yet, one of the main drawbacks of graph representation is that the computation of standard graph similarity measures is exponential in the number of involved nodes. Hence, such computations are feasible for small graphs only. The present paper considers the problem of graph isomorphism, i.e. checking two graphs for identity. A novel approach for the efficient computation of graph isomorphism is presented. The proposed algorithm is based on bipartite graph matching by means of Munkres' algorithm. The algorithmic framework is suboptimal in the sense of possibly rejecting pairs of graphs without making a decision. As an advantage, however, it offers polynomial runtime. In experiments on two TC-15 graph sets we demonstrate substantial speedups of our proposed method over several standard procedures for graph isomorphism, such as Ullmann's method, the VF2 algorithm, and Nauty. Furthermore, although the computational framework for isomorphism is suboptimal, we show that the proposed algorithm rejects only very few pairs of graphs.