| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 402949 | Journal of Symbolic Computation | 2016 | 13 Pages |
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.
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Physical Sciences and Engineering
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Artificial Intelligence
Authors
Elizaveta Frenkel, Andrey Nikolaev, Alexander Ushakov,