Efficiency of a Good But Not Linear Set Union Algorithm
Journal of the ACM (JACM)
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
A Subexponential Algorithm for Trivalent Graph Isomorphism
A Subexponential Algorithm for Trivalent Graph Isomorphism
Structure forest and composition factors for small base groups in nearly linear time
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Computing normalizers in permutation p-groups
ISSAC '94 Proceedings of the international symposium on Symbolic and algebraic computation
Hypergraph isomorphism and structural equivalence of Boolean functions
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Parallel subgraph matching on a hierarchical interconnection network
Hardware implementation of intelligent systems
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This paper describes an O(n3logn) deterministic algorithm and an O(n3) Las Vegas algorithm for testing whether two given trivalent graphs on n vertices are isomorphic. In fact, the algorithms construct the set of all isomorphisms between two such graphs, presenting, in particular, generators for the group of all automorphisms of a trivalent graph. The algorithms are based upon the original polynomial-time solution to these problems by Luks but they introduce numerous speedups. These include improved permutation-group algorithms that exploit the structure of the underlying 2-groups. A remarkable property of the Las Vegas algorithm is that it computes the set of all isomorphisms between two trivalent graphs for the cost of computing only those isomorphisms that map a specified edge to a specified edge.