# Graph isomorphism in quasipolynomial time [extended abstract]

@article{Babai2016GraphII, title={Graph isomorphism in quasipolynomial time [extended abstract]}, author={L{\'a}szl{\'o} Babai}, journal={Proceedings of the forty-eighth annual ACM symposium on Theory of Computing}, year={2016} }

We show that the Graph Isomorphism (GI) problem and the more general problems of String Isomorphism (SI) andCoset Intersection (CI) can be solved in quasipolynomial(exp((logn)O(1))) time. The best previous bound for GI was exp(O( √n log n)), where n is the number of vertices (Luks, 1983); for the other two problems, the bound was similar, exp(O~(√ n)), where n is the size of the permutation domain (Babai, 1983). Following the approach of Luks’s seminal 1980/82 paper, the problem we actually…

## 250 Citations

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