Some bounds for the construction of Gro¨bner bases
Proceedings of the 4th International Conference, AAECC-4 on Applicable algebra, error-correcting codes, combinatorics and computer algebra
Coherent algebras and the graph isomorphism problem
Discrete Applied Mathematics - Combinatorics and complexity
The graph isomorphism problem: its structural complexity
The graph isomorphism problem: its structural complexity
Polynomial time algorithms for modules over finite dimensional algebras
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
On a New High Dimensional Weisfeiler-Lehman Algorithm
Journal of Algebraic Combinatorics: An International Journal
Geometric Complexity Theory I: An Approach to the P vs. NP and Related Problems
SIAM Journal on Computing
Isomorphism of graphs with bounded eigenvalue multiplicity
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Linear time algorithm for isomorphism of planar graphs (Preliminary Report)
STOC '74 Proceedings of the sixth annual ACM symposium on Theory of computing
Isomorphism testing for graphs of bounded genus
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
A polynomial-time algorithm for determining the isomorphism of graphs of fixed genus
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
Parallel algorithms for permutation groups and graph isomorphism
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
Geometric Complexity Theory II: Towards Explicit Obstructions for Embeddings among Class Varieties
SIAM Journal on Computing
A V log V algorithm for isomorphism of triconnected planar graphs
Journal of Computer and System Sciences
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It is unknown whether two graphs can be tested for isomorphism in polynomial time. A classical approach to the Graph Isomorphism Problem is the d-dimensional Weisfeiler-Lehman algorithm. The d-dimensional WL-algorithm can distinguish many pairs of graphs, but the pairs of non-isomorphic graphs constructed by Cai, Furer and Immerman it cannot distinguish. If d is fixed, then the WL-algorithm runs in polynomial time. We will formulate the Graph Isomorphism Problem as an Orbit Problem: Given a representation V of an algebraic group G and two elements v"1,v"2@?V, decide whether v"1 and v"2 lie in the same G-orbit. Then we attack the Orbit Problem by constructing certain approximate categories C"d, d@?N={1,2,3,...} whose objects include the elements of V. We show that v"1 and v"2 are not in the same orbit by showing that they are not isomorphic in the category C"d for some d@?N. For every d this gives us an algorithm for isomorphism testing. We will show that the WL-algorithms reduce to our algorithms, but that our algorithms cannot be reduced to the WL-algorithms. Unlike the Weisfeiler-Lehman algorithm, our algorithm can distinguish the Cai-Furer-Immerman graphs in polynomial time.