### Abstract

Language | English |
---|---|

Pages | 17-32 |

Journal | Informatica |

Volume | 26 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2015 |

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### Cite this

*Informatica*,

*26*(1), 17-32. https://doi.org/10.15388/Informatica.2015.36

}

*Informatica*, vol. 26, no. 1, pp. 17-32. https://doi.org/10.15388/Informatica.2015.36

**On the minimum number of simplex shapes in longest edge bisection refinement of a regular n-simplex.** / Aparicio, G.; Casado, L.G.; Hendrix, E.M.T.; Toth, B.G.; García, I.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - On the minimum number of simplex shapes in longest edge bisection refinement of a regular n-simplex

AU - Aparicio, G.

AU - Casado, L.G.

AU - Hendrix, E.M.T.

AU - Toth, B.G.

AU - García, I.

PY - 2015

Y1 - 2015

N2 - 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. This process generates simplices belonging to different shape classes. Having less simplex shapes facilitates the prediction of the further workload from a node in the binary tree, because the same shape leads to the same sub-tree. Irregular sub-simplices generated in the refinement process may have more than one longest edge when n\geqslant 3. The question is how to choose the longest edge to be bisected such that the number of shape classes is as small as possible. We develop a Branch-and-Bound (B&B) algorithm to find the minimum number of classes in the refinement process. The developed B&B algorithm provides a minimum number of eight classes for a regular 3-simplex. Due to the high computational cost of solving this combinatorial problem, future research focuses on using high performance computing to derive the minimum number of shapes in higher dimensions.

AB - 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. This process generates simplices belonging to different shape classes. Having less simplex shapes facilitates the prediction of the further workload from a node in the binary tree, because the same shape leads to the same sub-tree. Irregular sub-simplices generated in the refinement process may have more than one longest edge when n\geqslant 3. The question is how to choose the longest edge to be bisected such that the number of shape classes is as small as possible. We develop a Branch-and-Bound (B&B) algorithm to find the minimum number of classes in the refinement process. The developed B&B algorithm provides a minimum number of eight classes for a regular 3-simplex. Due to the high computational cost of solving this combinatorial problem, future research focuses on using high performance computing to derive the minimum number of shapes in higher dimensions.

U2 - 10.15388/Informatica.2015.36

DO - 10.15388/Informatica.2015.36

M3 - Article

VL - 26

SP - 17

EP - 32

JO - Informatica

T2 - Informatica

JF - Informatica

SN - 0868-4952

IS - 1

ER -