Hitting Set
Pedagogical Contributions for Learning within the Scope of Theory of Computation
DOI:
https://doi.org/10.20873/uft.2675-3588.2026.v7n2.p71-80Keywords:
Hitting Set, NP-Complete, Vertex Cover, Polynomial Reduction, Theory of ComputationAbstract
This paper presents a pedagogical approach to the study of the Hitting Set problem, aiming to reproduce and make accessible the classic demonstration of its NP-completeness, as established in the specialized literature. Unlike works aiming to propose novel theoretical results, the central objective of this research is to bridge a didactic gap by meticulously detailing the polynomial reduction from the Vertex Cover problem to the Hitting Set problem. The adopted methodology begins with a review of fundamental concepts, including formal definitions of the P and NP classes, as well as the concepts of certificates and efficient verification. Subsequently, a proof inspired by Richard Karp is constructed step-by-step, emphasizing the visualization of transforming graph instances into set collections using “before and after” diagrams. Additionally, the “Observer's Dilemma” is introduced—an original analogy to illustrate combinatorial complexity. Finally, practical applications in bioinformatics and software engineering are discussed, consolidating the material as an effective support resource for teaching Theory of Computation.
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Copyright (c) 2026 João Pedro Melo Póvoa, Benedito Jaime Melo Moraes Junior, Daniel Martins da Silva, Tanilson Dias dos Santos
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