Perspectives of Monge properties in optimization
Discrete Applied Mathematics
On the boolean minimal realization problem in the max-plus algebra
Systems & Control Letters
An O(n2) algorithm for maximum cycle mean of Monge matrices in max-algebra
Discrete Applied Mathematics
Structure and dimension of the eigenspace of a concave Monge matrix
Discrete Applied Mathematics
Note: Computing an eigenvector of an inverse Monge matrix in max-plus algebra
Discrete Applied Mathematics
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In this paper we consider cyclic flow-shop system, which dynamics can be described by the max-plus vector equation of the form s(k + 1) = D ⊗ s(k), where D is the Dynamics matrix of the system calculated from processing times of operations. The method for finding D in O(nm2) time is presented. We prove that D fulfills the inverse Monge property, i.e. dij + dkl ≥ dil + dkj for any i k, j l. We do this by introducing the concept of i/o graph. I/o graphs can be used for modeling max-plus linear discrete event systems. We show the relation between structural properties of i/o graph and the inverse Monge properties of its corresponding matrix. The period of the system equals max-plus algebraic eigenvalue of D and, since D is an inverse Monge matrix, its max-plus algebraic eigenvalue can be found in just O(m) time [1].