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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2018.32
URN: urn:nbn:de:0030-drops-85201
URL: http://drops.dagstuhl.de/opus/volltexte/2018/8520/
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Ganardi, Moses ; König, Daniel ; Lohrey, Markus ; Zetzsche, Georg

Knapsack Problems for Wreath Products

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LIPIcs-STACS-2018-32.pdf (0.5 MB)


Abstract

In recent years, knapsack problems for (in general non-commutative) groups have attracted attention. In this paper, the knapsack problem for wreath products is studied. It turns out that decidability of knapsack is not preserved under wreath product. On the other hand, the class of knapsack-semilinear groups, where solutions sets of knapsack equations are effectively semilinear, is closed under wreath product. As a consequence, we obtain the decidability of knapsack for free solvable groups. Finally, it is shown that for every non-trivial abelian group G, knapsack (as well as the related subset sum problem) for the wreath product G \wr Z is NP-complete.

BibTeX - Entry

@InProceedings{ganardi_et_al:LIPIcs:2018:8520,
  author =	{Moses Ganardi and Daniel K{\"o}nig and Markus Lohrey and Georg Zetzsche},
  title =	{{Knapsack Problems for Wreath Products}},
  booktitle =	{35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)},
  pages =	{32:1--32:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-062-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{96},
  editor =	{Rolf Niedermeier and Brigitte Vall{\'e}e},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8520},
  URN =		{urn:nbn:de:0030-drops-85201},
  doi =		{10.4230/LIPIcs.STACS.2018.32},
  annote =	{Keywords: knapsack, wreath products, decision problems in group theory}
}

Keywords: knapsack, wreath products, decision problems in group theory
Seminar: 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)
Issue Date: 2018
Date of publication: 20.02.2018


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