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Heuristics to Reduce the Number of Simplices in Longest Edge Bisection Refinement of a Regular n-Simplex

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Computational Science and Its Applications – ICCSA 2014 (ICCSA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8580))

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Abstract

In several areas like Global Optimization using branch-and-bound methods, the unit n-simplex is refined by bisecting the longest edge such that a binary search tree appears. The refinement usually selects the first longest edge and ends when the size of the sub-simplices generated in the refinement is smaller than a given accuracy. Irregular sub-simplices may have more than one longest edge only for n ≥ 3. The question is how to choose the longest edge to be bisected such that the number of sub-simplices in the generated binary tree is minimal. The difficulty of this Combinatorial Optimization problem increases with n. Therefore, heuristics are studied that aim to minimize the number of generated simplices.

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Author information

Authors and Affiliations

  1. TIC 146: Supercomputing-Algorithms Research Group, Universidad de Almería, Agrifood Campus of International Excellence (ceiA3), 04120, Spain

    Guillermo Aparicio

  2. Department of Informatics, University of Almería, Agrifood Campus of International Excellence (ceiA3), 04120, Spain

    Leocadio G. Casado

  3. Department of Differential Equations, Budapest University of Technology and Economics, Egry J. u. 1., Budapest, 1111, Hungary

    Boglárka G-Tóth

  4. Department of Computer Architecture, Universidad de Málaga, Campus de Teatinos, 29017, Spain

    Eligius M. T. Hendrix & Inmaculada García

Authors
  1. Guillermo Aparicio
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  2. Leocadio G. Casado
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  3. Boglárka G-Tóth
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  4. Eligius M. T. Hendrix
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  5. Inmaculada García
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Editor information

Editors and Affiliations

  1. School of Engineering, University of Basilicata, 85100, Potenza, Italy

    Beniamino Murgante

  2. Department of Computer and Information Sciences, Covenant University, Ota, Nigeria

    Sanjay Misra

  3. Department of Production and Systems, University of Minho, 4710-057, Braga, Portugal

    Ana Maria A. C. Rocha

  4. DICAR, Polytecnico di Bari, 70125, Bari, Italy

    Carmelo Torre

  5. University of Minho, Braga, Portugal

    Jorge Gustavo Rocha  & Maria Irene Falcão  & 

  6. Monash University, 3800, Clayton, VIC, Australia

    David Taniar

  7. Department of Intelligent Informatics, Kyushu Sangyo University, 2-3-1 Matsukadai, 813-8503, Higashi-ku, Fukuoka, Japan

    Bernady O. Apduhan

  8. Department of Mathematics and Computer Science, University of Perugia, Via Vanvitelli, 1, 06123, Perugia, Italy

    Osvaldo Gervasi

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© 2014 Springer International Publishing Switzerland

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Aparicio, G., Casado, L.G., G-Tóth, B., Hendrix, E.M.T., García, I. (2014). Heuristics to Reduce the Number of Simplices in Longest Edge Bisection Refinement of a Regular n-Simplex. In: Murgante, B., et al. Computational Science and Its Applications – ICCSA 2014. ICCSA 2014. Lecture Notes in Computer Science, vol 8580. Springer, Cham. https://doi.org/10.1007/978-3-319-09129-7_9

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  • DOI: https://doi.org/10.1007/978-3-319-09129-7_9

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-09128-0

  • Online ISBN: 978-3-319-09129-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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