• A
  • A
  • A
  • ABC
  • ABC
  • ABC
  • А
  • А
  • А
  • А
  • А
Regular version of the site

Article

The complexity of tropical matrix factorization

Advances in Mathematics. 2014. Vol. 254. P. 138-156.

The tropical arithmetic operations on R are defined by a⊕b=min{a, b} and a⊗b=a+b. Let A be a tropical matrix and k a positive integer, the problem of Tropical Matrix Factorization (TMF) asks whether there exist tropical matrices B∈R^{m×k} and C∈R^{k×n} satisfying B⊗C=A. We show that no algorithm for TMF is likely to work in polynomial time for every fixed k, thus resolving a problem proposed by Barvinok in 1993.