Does co-NP have short interactive proofs?
Information Processing Letters
Graph isomorphism is in the low hierarchy
Journal of Computer and System Sciences
An Algorithm for Subgraph Isomorphism
Journal of the ACM (JACM)
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Improved random graph isomorphism
Journal of Discrete Algorithms
Canonical labelling of graphs in linear average time
SFCS '79 Proceedings of the 20th Annual Symposium on Foundations of Computer Science
Isomorphism Testing via Polynomial-Time Graph Extensions
Journal of Mathematical Modelling and Algorithms
A consistency rule for graph isomorphism problem
Proceedings of the 27th Annual ACM Symposium on Applied Computing
Practical graph isomorphism, II
Journal of Symbolic Computation
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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 logn ) 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 *** [*** (ln 4 n / n ln ln n ), 1 *** *** (ln 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.