Abstract
In this paper we continue along the same line of research started in earlier works, towards to providing a categorical view of structural complexity to optimization problems. The main aim is to provide a universal language for supporting formalisms to specify the hierarchy approximation system for an abstract NP-hard optimization problem. Categorical shape theory provides the mathematical framework to deal with approximation, enabling comparison of objects of interest and of models. In this context, tractable optimization problems are considered as a class of “models” or “prototypes” within a larger class of objects of interest – the intractable optimization problems class. Standard categorial constructions like universal objects, functors and adjunctions allow to formalize an approximation hierarchy system to optimization problems, besides characterizing NP-hard optimization problems as concrete universal objects.
This work is partially supported by FAPERGS and CNPq.
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dos Santos Leal, L.A., Claudio, D.M., Toscani, L.V., Menezes, P.B. (2005). Approximation Problems Categories. In: Moreno Díaz, R., Pichler, F., Quesada Arencibia, A. (eds) Computer Aided Systems Theory – EUROCAST 2005. EUROCAST 2005. Lecture Notes in Computer Science, vol 3643. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11556985_2
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