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Graph Isomorphism in Quasipolynomial Time
TLDR
The algorithm builds on Luks’s SI framework and attacks the barrier configurations for Luks's algorithm by group theoretic “local certificates” and combinatorial canonical partitioning techniques and shows that in a well-defined sense, Johnson graphs are the only obstructions to effective canonical partitioned.Abstract:
We show that the Graph Isomorphism (GI) problem and the related problems of String Isomorphism (under group action) (SI) and Coset Intersection (CI) can be solved in quasipolynomial (exp (logn) O(1) � ) time. The best previous bound for GI was exp(O( √ nlogn)), where n is the number of vertices (Luks, 1983); for the other two problems, the bound was similar, exp( e O( √ n)), where n is the size of the permutation domain (Babai, 1983). The algorithm builds on Luks’s SI framework and attacks the barrier configurations for Luks’s algorithm by group theoretic “local certificates” and combinatorial canonical partitioning techniques. We show that in a well-defined sense, Johnson graphs are the only obstructions to effective canonical partitioning.read more
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References
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Journal ArticleDOI
Practical graph isomorphism, II
Brendan D. McKay,Adolfo Piperno +1 more
TL;DR: Traces as mentioned in this paper is a graph isomorphism algorithm based on the refinement-individualization paradigm, and it is implemented in several of the key implementations of the program nauty.
Book
The Subgroup Structure of the Finite Classical Groups
TL;DR: In this article, a unified treatment of the theory of geometric subgroups of the classical groups, introduced by Aschbacher, is presented, and the questions of maximality and conjugacy of these groups are answered.
Journal ArticleDOI
Isomorphism of graphs of bounded valence can be tested in polynomial time
TL;DR: In this paper, it was shown that testing isomorphism of graphs of bounded valance is polynomial-time reducible to the color automorphism problem for groups with composition factors of bounded order.