2 citations · 5 across the 6 of their papers we have counts for
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On max-plus two-sided linear systems whose solution sets are min-plus linear
Yasutaka Ooga, Yuki Nishida, Yoshihide Watanabe
The max-plus algebra is defined in terms of a combination of the following two operations: addition, , and multiplication, $a…
Independence and orthogonality of algebraic eigenvectors over the max-plus algebra
Yuki Nishida, Sennosuke Watanabe, Yoshihide Watanabe
The max-plus algebra is a semiring with the two operations: addition and multiplication . Roots of the…
Network Simplex Algorithm associated with the Maximum Flow Problem
Sennosuke Watanabe, Hodaka Tanaka, Yoshihide Watanabe
In the present paper, we apply the network simplex algorithm for solving the minimum cost flow problem, to the maximum flow problem. Then we prove that the cycling phenomenon which…
Two characteristic polynomials corresponding to graphical networks over min-plus algebra
Sennosuke Watanabe, Yuto Tozuka, Yoshihide Watanabe +2
In this paper, we investigate characteristic polynomials of matrices in min-plus algebra. Eigenvalues of min-plus matrices are known to be the minimum roots of the characteristic p…