Scheduling Problems
Pedagogical Contributions to Learning within the Scope of Computation Theory
DOI:
https://doi.org/10.20873/uft.2675-3588.2026.v7n2.p51-60Keywords:
NP-completeness, Scheduling, Polynomial reduction, 3-SAT, Computational complexityAbstract
Scheduling problems constitute a fundamental class of challenges in optimization and computing, particularly in operating systems, parallel processing, and real-time applications. Despite their wide practical use, many variants remain computationally intractable, even under strong structural restrictions. This article investigates the NP-completeness of two specific versions of the scheduling problem: scheduling with unit processing time and scheduling on two processors with tasks of duration one or two time units. The theoretical foundation relies on classical polynomial-time reductions, especially from the 3-SAT problem, which allows logical assignments to be encoded directly into precedence constraints and processor-capacity limitations. Furthermore, additional transformations between restricted versions of the problem are employed to preserve the structural equivalence of solutions. The contributions include a didactic reconstruction of the original proofs, an analysis of the mechanisms that give rise to computational hardness, and a discussion of the practical implications of these results in real scheduling systems. The results presented in the literature reinforce that even seemingly simple scenarios exhibit NP-complete behavior.
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Copyright (c) 2026 Heloisa Rolins Ribeiro, Neci Oneides da Silva Fialho Neta, Daniel Martins da Silva, Tanilson Dias dos Santos
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