Non-commutative lattice problems
Group Theory
2015-08-12 v1 Computational Complexity
Combinatorics
Abstract
We consider several subgroup-related algorithmic questions in groups, modeled after the classic computational lattice problems, and study their computational complexity. We find polynomial time solutions to problems like finding a subgroup element closest to a given group element, or finding a shortest non-trivial element of a subgroup in the case of nilpotent groups, and a large class of surface groups and Coxeter groups. We also provide polynomial time algorithm to compute geodesics in given generators of a subgroup of a free group.
Cite
@article{arxiv.1508.02388,
title = {Non-commutative lattice problems},
author = {Alexei Myasnikov and Andrey Nikolaev and Alexander Ushakov},
journal= {arXiv preprint arXiv:1508.02388},
year = {2015}
}
Comments
17 pages, 2 figures