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A Categorical Approach to NP-Hard Optimization Problems

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Computer Aided Systems Theory - EUROCAST 2003 (EUROCAST 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2809))

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Abstract

Aiming at developing a theoretical framework for the formal study of NP-hard optimization problems, which is built on precise mathematical foundations, we have focused on structural properties of optimization problems related to approximative issue. From the observation that, intuitively, there are many connections among categorical concepts and structural complexity notions, in this work we present a categorical approach to cope with some questions originally studied within Computational Complexity Theory. After defining the polynomial time soluble optimization problems category OPTS and the optimization problems category OPT, a comparison mechanism between them and an approximation system to each optimization problem have been introduced, following the basic idea of categorical shape theory. In this direction, we consider new insights and a deeper understanding of some basic questions inside the Structural Complexity field, by an universal language.

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Author information

Authors and Affiliations

  1. Mathematics Department, PUCRS, Porto Alegre, Brazil

    Liara Aparecida dos Santos Leal & Dalcidio Moraes Claudio

  2. Computing Institute, UFRGS, Porto Alegre, Brazil

    Laira Vieira Toscani & Paulo Blauth Menezes

Authors
  1. Liara Aparecida dos Santos Leal
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  2. Dalcidio Moraes Claudio
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  3. Laira Vieira Toscani
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  4. Paulo Blauth Menezes
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Editor information

Editors and Affiliations

  1. Institute of Cybernetics, Universidad de Las Palmas de Gran Canaria, Spain

    Roberto Moreno-Díaz

  2. Systems Theory, Johannes Kepler University Linz, Altenbergerstrasse 69, A-4040, Linz, Austria

    Franz Pichler

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© 2003 Springer-Verlag Berlin Heidelberg

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dos Santos Leal, L.A., Moraes Claudio, D., Vieira Toscani, L., Blauth Menezes, P. (2003). A Categorical Approach to NP-Hard Optimization Problems. In: Moreno-Díaz, R., Pichler, F. (eds) Computer Aided Systems Theory - EUROCAST 2003. EUROCAST 2003. Lecture Notes in Computer Science, vol 2809. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45210-2_7

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  • DOI: https://doi.org/10.1007/978-3-540-45210-2_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20221-9

  • Online ISBN: 978-3-540-45210-2

  • eBook Packages: Springer Book Archive

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