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- W1979581330 abstract "Abstract The smallest integer k for which the elements of a real matrix A can be expressed as A i j = min t = 1 k { B i t + C t j } with B ∈ R m × k and C ∈ R k × n is called the combinatorial rank of A. This notion was introduced by Barvinok in 1993, and he posed a problem on the complexity of detecting matrices with combinatorial rank equal to a fixed integer k. Fast algorithms solving this problem have been known only for k ≤ 2 , and we construct an algorithm that decides whether or not a given matrix has combinatorial rank three in time O ( ( m + n ) 3 m n log ( m n ) ) ." @default.
- W1979581330 created "2016-06-24" @default.
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- W1979581330 date "2014-08-01" @default.
- W1979581330 modified "2023-09-29" @default.
- W1979581330 title "Detecting matrices of combinatorial rank three" @default.
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- W1979581330 doi "https://doi.org/10.1016/j.jcta.2014.05.001" @default.
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