Paper Info
Title
Graph Isomorphism in Quasipolynomial Time
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 ($\exp((\log n)^{O(1)})$) time. The best previous bound for GI was $\exp(O(\sqrt{n\log n}))$, where $n$ is the number of vertices (Luks, 1983); for the other two problems, the bound was similar, $\exp(\tilde{O}(\sqrt{n}))$, 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. Luks's barrier situation is characterized by a homomorphism {\phi} that maps a given permutation group $G$ onto $S_k$ or $A_k$, the symmetric or alternating group of degree $k$, where $k$ is not too small. We say that an element $x$ in the permutation domain on which $G$ acts is affected by {\phi} if the {\phi}-image of the stabilizer of $x$ does not contain $A_k$. The affected/unaffected dichotomy underlies the core "local certificates" routine and is the central divide-and-conquer tool of the algorithm.
Year
Venue
Field
2015
CoRR
Discrete mathematics,Graph,Combinatorics,Vertex (geometry),Graph isomorphism,Permutation,Isomorphism,Coset,Graph isomorphism problem,Mathematics
DocType
Volume
Citations 
Journal
abs/1512.03547
67
PageRank 
References 
Authors
2.64
14
1
Name
Order
Citations
PageRank
Laszlo Babai13537573.58