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The complexity of tropical matrix factorization

Advances in Mathematics. 2014. Vol. 254. P. 138–156.
Shitov Y.

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.

Priority areas: mathematics
Language: English
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Keywords: вычислительная сложностьmatrix factorizationstropical semiringтропическое полукольцофакторизация матрицComputational Complexity
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