Skip to main content
SpringerLink
Log in

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

  • Conference paper
Book cover Computational Science and Its Applications – ICCSA 2014 (ICCSA 2014)

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

Included in the following conference series:

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Adler, A.: On the Bisection Method for Triangles. Mathematics of Computation 40(162), 571–574 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  2. Aparicio, G., Casado, L.G., Hendrix, E.M.T., G.-Tóth, B., García, I.: On the minimum number of simplex classes in longest edge bisection refinement of a regular n-simplex. Informatica (submitted)

    Google Scholar 

  3. Aparicio, G., Casado, L.G., Hendrix, E.M.T., García, I., G.-Tóth, B.: On computational aspects of a regular n-simplex bisection. In: Proceedings of the 2013 Eighth International Conference on P2P, Parallel, Grid, Cloud and Internet Computing, Compiegne, France, pp. 513–518 (October 2013)

    Google Scholar 

  4. Ashayeri, J., van Eijs, A., Nederstigt, P.: Blending modelling in a process manufacturing: A case study. European Journal of Operational Research 72(3), 460–468 (1994)

    Article  Google Scholar 

  5. Casado, L.G., García, I., G.-Tóth, B., Hendrix, E.M.T.: On determining the cover of a simplex by spheres centered at its vertices. Journal of Global Optimization 50(4), 645–655 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  6. Hannukainen, A., Korotov, S., Křížek, M.: On numerical regularity of the face-to-face longest-edge bisection algorithm for tetrahedral partitions. Science of Computer Programming 90(A), 34–41 (2014)

    Article  Google Scholar 

  7. Horst, R.: On generalized bisection of n-simplices. Mathematics of Computation 66(218), 691–698 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  8. Mitchell, W.F.: A comparison of adaptive refinement techniques for elliptic problems. ACM Trans. Math. Softw. 15(4), 326–347 (1989)

    Article  MATH  Google Scholar 

Download references

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
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Leocadio G. Casado
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Boglárka G-Tóth
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Eligius M. T. Hendrix
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Inmaculada García
    View author publications

    You can also search for this author in PubMed Google Scholar

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

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

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

Download citation

  • 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)

Publish with us

Policies and ethics

Search

Navigation