The Complexity of Knapsack in Graph Groups
نویسندگان
چکیده
Myasnikov et al. have introduced the knapsack problem for arbitrary finitely generated groups. In [24] 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 TCcomplete for complete graphs, it is LogCFL-complete for each (non-complete) transitive forest. For every remaining graph, the problem is NP-complete.
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