The Complexity of Knapsack in Graph Groups

Authors Markus Lohrey, Georg Zetzsche

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Markus Lohrey
Georg Zetzsche

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Markus Lohrey and Georg Zetzsche. The Complexity of Knapsack in Graph Groups. In 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 66, pp. 52:1-52:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


Myasnikov et al. have introduced the knapsack problem for arbitrary finitely generated groups. In LohreyZ16 the authors proved that for each graph group, the knapsack problem can be solved in NP. Here, we determine the exact complexity of the problem for every graph group. While the problem is TC^0-complete for complete graphs, it is LogCFL-complete for each (non-complete) transitive forest. For every remaining graph, the problem is NP-complete.
  • knapsack
  • subset sum
  • graph groups
  • decision problems in group theory


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