We show that, generically, finding the k-th root of a braid is very fast. More precisely, we provide an algorithm which, given a braid x on n strands and canonical length l, and an integer k>1, computes a k-th root of x, if it exists, or guarantees that such a root does not exist. The generic-case complexity of this algorithm is O(l(l+n)n3logn). The non-generic cases are treated using a previously known algorithm by Sang-Jin Lee.
Cite
@article{arxiv.1909.10962,
title = {The root extraction problem for generic braids},
author = {María Cumplido and Juan González-Meneses and Marithania Silvero},
journal= {arXiv preprint arXiv:1909.10962},
year = {2019}
}