Fixed-parameter tractability of canonical polyadic decomposition over finite fields

TL;DR

This paper proves that computing a rank-R canonical polyadic decomposition of a 3D tensor over a finite field is fixed-parameter tractable, providing a new theoretical understanding of the problem's complexity.

Contribution

The authors present a simple proof establishing fixed-parameter tractability for tensor decomposition over finite fields, along with an upper bound on the algorithm's time complexity.

Findings

Fixed-parameter tractability established for tensor decomposition over finite fields

Provided a nontrivial upper bound on the problem's computational complexity

Simplified proof technique for the tractability result

Abstract

We present a simple proof that finding a rank-$R$ canonical polyadic decomposition of a 3-dimensional tensor over a finite field $\mathbb{F}$ is fixed-parameter tractable with respect to $R$ and $\mathbb{F}$. We also show a nontrivial upper bound on the time complexity of this problem.