2. Connections Between Artificial Intelligence and Computational Complexity and the Complexity of Graphs

  1. Matthias Dehmer2,
  2. Abbe Mowshowitz3 and
  3. Frank Emmert-Streib3
  1. Ángel Garrido

Published Online: 12 JUL 2013

DOI: 10.1002/9783527670468.ch02

Advances in Network Complexity

Advances in Network Complexity

How to Cite

Garrido, Á. (2013) Connections Between Artificial Intelligence and Computational Complexity and the Complexity of Graphs, in Advances in Network Complexity (eds M. Dehmer, A. Mowshowitz and F. Emmert-Streib), Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, Germany. doi: 10.1002/9783527670468.ch02

Editor Information

  1. 2

    UMIT, Institut für Bioinformatik und, Translationale Forschung, Eduard-Wallnöfer-Zentrum 1, 6060 Hall in Tyrol, Austria

  2. 3

    The City College of New York, Department of Computer Science, 138th Street at Convent Avenue, New York, NY 10031, USA

Author Information

  1. Faculty of Sciences UNED, Department of Fundamental Mathematics, Paseo Senda del Rey, 9, 28040, Madrid, Spain

Publication History

  1. Published Online: 12 JUL 2013
  2. Published Print: 10 JUL 2013

ISBN Information

Print ISBN: 9783527332915

Online ISBN: 9783527670468

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Keywords:

  • searching methods;
  • representation methods;
  • heuristics;
  • fuzzy measures;
  • graph theory;
  • AI;
  • fuzzy modeling and optimization;
  • fuzzy systems;
  • computational intelligence

Summary

Computational complexity (CC) and graph complexity is an important field of research generally on mathematics and, in particular, on theoretical computer science, that focuses on classifying computational problems based on the amount of resources they require. Examples of such resources include time, space, communication, amount of randomness, and so on. This field has introduced many interesting computational models to study such problems and has been the source of amazing results in the recent years leading to a deeper understanding of the power and limitations of efficient computation. The CC has to provide that it is possible to reduce – many times notably – across the observation of conditions such as the symmetry, as it is done, for instance, in the equations of Physics. Something that is really very useful, besides the mathematical consequences that could stem from it. The main tool necessary for this framework will be graph theory. Also, the connections to graph complexity will be also discussed.