A fast algorithm for testing isomorphism of permutation networks

The problem of deciding whether two given permutation sequences are conjugate is addressed. The author exhibits an algorithm that solves this problem in time O(N log N), where N is the sum of the sizes of the two sequences. The algorithm can be applied to the problem of deciding whether two permutation networks are equivalent. The time bound for the algorithm is a significant improvement over the O(N²) bound of the algorithm due to Y.A. Oruc and M.Y. Oruc (1985). The author´s method applies techniques used by the Hopcroft-Tarjan algorithm for deciding planar graph isomorphism