Knapsack problems in products of groups
Group Theory
2015-08-11 v2 Computational Complexity
Abstract
The classic knapsack and related problems have natural generalizations to arbitrary (non-commutative) groups, collectively called knapsack-type problems in groups. We study the effect of free and direct products on their time complexity. We show that free products in certain sense preserve time complexity of knapsack-type problems, while direct products may amplify it. Our methods allow to obtain complexity results for rational subset membership problem in amalgamated free products over finite subgroups.
Keywords
Cite
@article{arxiv.1408.6509,
title = {Knapsack problems in products of groups},
author = {Elizaveta Frenkel and Andrey Nikolaev and Alexander Ushakov},
journal= {arXiv preprint arXiv:1408.6509},
year = {2015}
}
Comments
15 pages, 5 figures. Updated to include more general results, mostly in Section 4