arXiv (Cornell University)· 2012· Preprint
Knapsack in Graph Groups, HNN-Extensions and Amalgamated Products
- 371citations
- 2012year
Short summary
The knapsack problem, previously defined for general finitely generated groups, is now solvable in NP for graph groups, even with compressed group element representations.
AI-generated from the title and abstract; the full text is not read.
Key points
- The knapsack problem is solvable in NP for graph groups.
- This result applies even when group elements are represented by SLPs.
- NP-membership for the knapsack problem transfers to specific group extensions and products.
AI-generated from the title and abstract; the full text is not read.
Abstract
It is shown that the knapsack problem, which was introduced by Myasnikov et al. for arbitrary finitely generated groups, can be solved in NP for graph groups. This result even holds if the group elements are represented in a compressed form by SLPs, which generalizes the classical NP-completeness result of the integer knapsack problem. We also prove general transfer results: NP-membership of the knapsack problem is passed on to finite extensions, HNN-extensions over finite associated subgroups, and amalgamated products with finite identified subgroups.
The authors' abstract, as published at the source. arXiv (Cornell University), 2012 · DOI ↗
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Field: Geometry and Topology
Geometry and TopologyMathematics