A family of polycyclic groups over which the uniform conjugacy problem is NP-complete
This addresses a fundamental problem in computational group theory for researchers, showing that the conjugacy problem can be computationally intractable in certain groups.
The authors tackled the computational complexity of the conjugacy problem in polycyclic groups by constructing groups where this problem is at least as hard as the subset sum problem, proving it is NP-complete with parameters based on group size and input length.
In this paper we study the conjugacy problem in polycyclic groups. Our main result is that we construct polycyclic groups $G_n$ whose conjugacy problem is at least as hard as the subset sum problem with $n$ indeterminates. As such, the conjugacy problem over the groups $G_n$ is NP-complete where the parameters of the problem are taken in terms of $n$ and the length of the elements given on input.