## Knapsack problems in groups

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- by Alexei Myasnikov, Andrey Nikolaev and Alexander Ushakov PDF
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**84**(2015), 987-1016 Request permission

## Abstract:

We generalize the classical knapsack and subset sum problems to arbitrary groups and study the computational complexity of these new problems. We show that these problems, as well as the bounded submonoid membership problem, are $\mathbf {P}$-time decidable in hyperbolic groups and give various examples of finitely presented groups where the subset sum problem is $\mathbf {NP}$-complete.## References

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## Additional Information

**Alexei Myasnikov**- Affiliation: Stevens Institute of Technology, Hoboken, New Jersey 07030
- Email: amiasnik@stevens.edu
**Andrey Nikolaev**- Affiliation: Stevens Institute of Technology, Hoboken, New Jersey 07030
- Email: anikolae@stevens.edu
**Alexander Ushakov**- Affiliation: Stevens Institute of Technology, Hoboken, New Jersey 07030
- MR Author ID: 788960
- Email: aushakov@stevens.edu
- Received by editor(s): March 29, 2012
- Received by editor(s) in revised form: February 19, 2013, June 7, 2013, and July 1, 2013
- Published electronically: July 30, 2014
- Additional Notes: The work of the first and third authors was partially supported by NSF grant DMS-0914773.
- © Copyright 2014 American Mathematical Society
- Journal: Math. Comp.
**84**(2015), 987-1016 - MSC (2010): Primary 03D15, 20F65, 20F10
- DOI: https://doi.org/10.1090/S0025-5718-2014-02880-9
- MathSciNet review: 3290972