This work presents a categorical approach to cope with some questions originally studied within Computational Complexity Theory. It proceeds a research with theoretical emphasis, aiming at characterising the structural properties of optimization problems, related to the approximative issue, by means of Category Theory. In order to achieve it, two new categories are defined: the OPT category, which objects are optimization problems and the morphisms are the reductions between them, and the APX category, that has approximation problems as objects and approximation-preserving reductions as morphisms. Following the basic idea of categorical shape theory, a comparison mechanism between these two categories is defined and a hierarchical structure of approximation to each optimization problem can be modelled. © 2011 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Dos Santos Leal, L. A., Menezes, P. B., Claudio, D. M., & Toscani, L. V. (2001). Optimization problems categories. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2178 LNCS, pp. 285–299). Springer Verlag. https://doi.org/10.1007/3-540-45654-6_23
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