A subquadratic algorithm for the simultaneous conjugacy problem

07/11/2020

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by   Andrej Brodnik, et al.

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The d-Simultaneous Conjugacy problem in the symmetric group S_n asks whether there exists a permutation τ∈ S_n such that b_j = τ^-1a_j τ holds for all j = 1,2,…, d, where a_1, a_2,… , a_d and b_1, b_2,… , b_d are given sequences of permutations in S_n. The time complexity of existing algorithms for solving the problem is O(dn^2). We show that for a given positive integer d the d-Simultaneous Conjugacy problem in S_n can be solved in o(n^2) time.