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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Knapsack problems in groups
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by Alexei Myasnikov, Andrey Nikolaev and Alexander Ushakov PDF
Math. Comp. 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