Abstract

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∈Rm×k and C∈Rk×n satisfying B⊗C=A. We show that the TMF problem is NP-hard for every k≥7 fixed in advance, thus resolving a problem proposed by Barvinok in 1993.

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