Publication detail

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

SADÍLEK, V. VOŘECHOVSKÝ, M.

Original Title

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

Type

journal article in Web of Science

Language

English

Original Abstract

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.

Keywords

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

Authors

SADÍLEK, V.; VOŘECHOVSKÝ, M.

Released

21. 9. 2018

Publisher

VGTU Press

ISBN

1392-3730

Periodical

Journal of civil engineering and management

Year of study

24

Number

5

State

Republic of Lithuania

Pages from

410

Pages to

423

Pages count

14

URL

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

Full text in the Digital Library

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"
}