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DOI: 10.4230/LIPIcs.STACS.2016.50
URN: urn:nbn:de:0030-drops-57512
URL: http://drops.dagstuhl.de/opus/volltexte/2016/5751/
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Lohrey, Markus ; Zetzsche, Georg

Knapsack in Graph Groups, HNN-Extensions and Amalgamated Products

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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.

BibTeX - Entry

@InProceedings{lohrey_et_al:LIPIcs:2016:5751,
  author =	{Markus Lohrey and Georg Zetzsche},
  title =	{{Knapsack in Graph Groups, HNN-Extensions and Amalgamated Products}},
  booktitle =	{33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)},
  pages =	{50:1--50:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-001-9},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{47},
  editor =	{Nicolas Ollinger and Heribert Vollmer},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/5751},
  URN =		{urn:nbn:de:0030-drops-57512},
  doi =		{10.4230/LIPIcs.STACS.2016.50},
  annote =	{Keywords: Graph groups, HNN-extensions, amalgamated products, knapsack}
}

Keywords: Graph groups, HNN-extensions, amalgamated products, knapsack
Seminar: 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)
Issue Date: 2016
Date of publication: 16.02.2016


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