License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2018.26
URN: urn:nbn:de:0030-drops-94309
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9430/
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Swernofsky, Joseph

Tensor Rank is Hard to Approximate

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LIPIcs-APPROX-RANDOM-2018-26.pdf (0.4 MB)

Abstract

We prove that approximating the rank of a 3-tensor to within a factor of 1 + 1/1852 - delta, for any delta > 0, is NP-hard over any field. We do this via reduction from bounded occurrence 2-SAT.

BibTeX - Entry

@InProceedings{swernofsky:LIPIcs:2018:9430,
  author =	{Joseph Swernofsky},
  title =	{{Tensor Rank is Hard to Approximate}},
  booktitle =	{Approximation, Randomization, and Combinatorial  Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)},
  pages =	{26:1--26:9},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-085-9},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{116},
  editor =	{Eric Blais and Klaus Jansen and Jos{\'e} D. P. Rolim and David Steurer},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9430},
  URN =		{urn:nbn:de:0030-drops-94309},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2018.26},
  annote =	{Keywords: tensor rank, high rank tensor, slice elimination, approximation algorithm, hardness of approximation}
}

Keywords: tensor rank, high rank tensor, slice elimination, approximation algorithm, hardness of approximation
Collection: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)
Issue Date: 2018
Date of publication: 13.08.2018

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