Tensor Rank is Hard to Approximate

Author Joseph Swernofsky

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Joseph Swernofsky
  • Kungliga Tekniska Högskolan, Lindstedtsvägen 3, Stockholm SE-100 44, Sweden

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Joseph Swernofsky. Tensor Rank is Hard to Approximate. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 116, pp. 26:1-26:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Problems, reductions and completeness
  • tensor rank
  • high rank tensor
  • slice elimination
  • approximation algorithm
  • hardness of approximation


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