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

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F22%3A00556580" target="_blank" >RIV/67985840:_____/22:00556580 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.dam.2022.03.008" target="_blank" >https://doi.org/10.1016/j.dam.2022.03.008</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.dam.2022.03.008" target="_blank" >10.1016/j.dam.2022.03.008</a>

Result language
angličtina
Original language name
The non-positive circuit weight problem in parametric graphs: A solution based on dioid theory
Original language description
We consider a parametric weighted directed graph in which every $arc (j, i)$ has weight of the form $w((j, i)) = max(P_{ij}+lambda, I{ij}-lambda,C_{ij} )$, where $lambda$ is a real parameter, and P, I and C are arbitrary square matrices with elements in $mathbb{R} cap { -infty}$. An algorithm is proposed that solves the Non-positive Circuit weight Problem (NCP) on this class of parametric graphs, which consists in fi nding all values of $lambda$ such that the graph does not contain circuits with positive weight. This problem, which generalizes other instances of the NCP previously investigated in the literature, has applications in the consistency analysis of a class of discrete-event systems called P-time event graphs. The proposed algorithm is based on max-plus algebra and formal languages, and improves the worst-case complexity of other existing approaches, achieving strongly polynomial time complexity $O(n^4)$ (where n is the number of nodes in the graph).
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
20205 - Automation and control systems

Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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