Fast Algorithm for Graph Isomorphism Testing

In this paper we present a novel approach to the graph isomorphism problem. We combine a direct approach, that tries to find a mapping between the two input graphs using backtracking, with a (possibly partial) automorphism precomputing that allows to prune the search tree. We propose an algorithm, conauto, that has a space complexity of O(n(2) log n) bits. It runs in time O(n(5)) with high probability if either one of the input graphs is a G(n,p) random graph, for p is an element of [omega (ln(4) n/n ln ln n), 1 - omega (In-4 n/n ln ln n)]. We compare the practical performance of conauto with other popular algorithms, with an extensive collection of problem instances. Our algorithm behaves consistently for directed, undirected, positive, and negative cases. Additionally, when it is slower than any of the other algorithms, it is only by a small factor.