Detail publikace

Evaluation of pairwise distances among points forming a regular orthogonal grid in a hypercube

SADÍLEK, V. VOŘECHOVSKÝ, M.

Originální název

Evaluation of pairwise distances among points forming a regular orthogonal grid in a hypercube

Typ

článek v časopise ve Web of Science, Jimp

Jazyk

angličtina

Originální abstrakt

Cartesian grid is a basic arrangement of points that form a regular orthogonal grid (ROG). In some applications, it is needed to evaluate all pairwise distances among ROG points. This paper focuses on ROG discretization of a unit hypercube of arbitrary dimension. A method for the fast enumeration of all pairwise distances and their counts for a high number of points arranged into high-dimensional ROG is presented. The proposed method exploits the regular and collapsible pattern of ROG to reduce the number of evaluated distances. The number of unique distances is identified and frequencies are determined using combinatorial rules. The measured computational speed-up compared to a naïve approach corresponds to the presented theoretical analysis. The proposed method and algorithm may find applications in various fields. The paper shows application focused on the behaviour of various distance measures with the motivation to find the lower bounds on the criteria of point distribution uniformity in Monte Carlo integration.

Klíčová slova

full factorial design, design of experiments, pairwise distances, Audze-Eglãjs criterion, optimization, periodic space

Autoři

SADÍLEK, V.; VOŘECHOVSKÝ, M.

Vydáno

21. 9. 2018

Nakladatel

VGTU Press

ISSN

1392-3730

Periodikum

Journal of civil engineering and management

Ročník

24

Číslo

5

Stát

Litevská republika

Strany od

410

Strany do

423

Strany počet

14

URL

https://www.tede.vgtu.lt/index.php/JCEM/article/view/5189

Plný text v Digitální knihovně

http://hdl.handle.net/11012/85339

BibTex

@article{BUT150120,
  author="Václav {Sadílek} and Miroslav {Vořechovský}",
  title="Evaluation of pairwise distances among points forming a regular orthogonal grid in a hypercube",
  journal="Journal of civil engineering and management",
  year="2018",
  volume="24",
  number="5",
  pages="410--423",
  doi="10.3846/jcem.2018.5189",
  issn="1392-3730",
  url="https://www.tede.vgtu.lt/index.php/JCEM/article/view/5189"
}