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Knapsack in Graph Groups, HNN-Extensions and Amalgamated Products

Authors Markus Lohrey, Georg Zetzsche

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Markus Lohrey
Georg Zetzsche

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Markus Lohrey and Georg Zetzsche. Knapsack in Graph Groups, HNN-Extensions and Amalgamated Products. In 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 47, pp. 50:1-50:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
https://doi.org/10.4230/LIPIcs.STACS.2016.50

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.
Keywords
  • Graph groups
  • HNN-extensions
  • amalgamated products
  • knapsack

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