PASCAL user manual and report
Linear time algorithm for isomorphism of planar graphs (Preliminary Report)
STOC '74 Proceedings of the sixth annual ACM symposium on Theory of computing
Computation with permutation groups
SYMSAC '71 Proceedings of the second ACM symposium on Symbolic and algebraic manipulation
Computing automorphism groups of error-correcting codes
IEEE Transactions on Information Theory
Backtrack search with isomorph rejection and consistency check
Journal of Symbolic Computation
Permutation group algorithms based on partitions, I: Theory and algorithms
Journal of Symbolic Computation - Special issue on computational group theory: part 2
A fast cyclic base change for permutation groups
ISSAC '92 Papers from the international symposium on Symbolic and algebraic computation
Application of genetic algorithms to the algebraic simplification of tensor polynomials
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Backtrack searching in the presence of symmetry
Nordic Journal of Computing
Pruning by Isomorphism in Branch-and-Cut
Proceedings of the 8th International IPCO Conference on Integer Programming and Combinatorial Optimization
Improving Bounds on the Football Pool Problem by Integer Programming and High-Throughput Computing
INFORMS Journal on Computing
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
Symmetric ILP: Coloring and small integers
Discrete Optimization
Practical graph isomorphism, II
Journal of Symbolic Computation
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Our aim is to present a practical algorithm for the isomorphism problem that can be easily adapted to any class of combinatorial objects. We investigate the underlying principles of backtrack algorithms that determine a canonical representative of a combinatorial object. We identify the parts of the algorithm that are dependent on the class of combinatorial objects and those parts that are independent of the class. An interface between the two parts is developed to provide a general backtrack algorithm for the isomorphism problem of combinatorial objects that incorporates the technique of branch-and-bound, and that also uses the automorphisms of the combinatorial object to prune the search tree. Our general algorithm incorporates from computational group theory an algorithm known as the base change algorithm. The base change algorithm allows one to recover as much information as possible about the automorphism group when a new branch of the search tree is processed. Thus, it can lead to greater pruning of the search tree. This work is intended to lead to a better understanding of the practical isomorphism algorithms. It is not intended as a contribution to the theoretical study of the complexity of the isomorphism problem.