Year: 2026
Type: article
Abstract: Precedence constraints are inequalities used to model time dependencies. In 1958, Gallai proved that a finite system of precedence constraints admits solutions if and only if the corresponding precedence graph does not contain positive-weight circuits. We show that this result extends naturally to the case of infinitely many constraints. We then analyze two specific classes of infinite precedence graphs – $$\mathbb {N}$$ -periodic and ultimately periodic graphs – and prove that the existence of solutions of their related constraints can be verified in strongly polynomial time. The obtained algorithms find applications in P-time event graphs, which are a subclass of P-time Petri nets able to model production systems under cyclic schedules where tasks need to be performed within given time windows.
Source: Discrete Event Dynamic Systems
Authors: Davide Zorzenon, Jörg Raisch
Institution: Technische Universität Berlin
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
OpenAlex ID: W7131065160