The non-positive circuit weight problem in parametric graphs: A solution based on dioid theory

Let us consider a parametric weighted directed graph in which every arc (j,i) has weight of the form w((j,i))=max(Pij+λ,Iij−λ,Cij), where λ is real parameter and P, I C are arbitrary square matrices with elements R∪{−∞}. In this paper, we design an algorithm that solves Non-positive Circuit Problem (NCP) on class graphs, consists finding all values such does not contain circuits positive weight. This problem, generalizes other instances NCP previously investigated literature, applications consistency analysis discrete-event systems called P-time event graphs. The proposed based max-plus algebra formal languages, improves worst-case complexity existing approaches, achieving strongly polynomial time O(n4) (where n number nodes graph).