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

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26110%2F18%3APU129085" target="_blank" >RIV/00216305:26110/18:PU129085 - isvavai.cz</a>

Result on the web

<a href="https://journals.vgtu.lt/index.php/JCEM/article/view/5189" target="_blank" >https://journals.vgtu.lt/index.php/JCEM/article/view/5189</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3846/jcem.2018.5189" target="_blank" >10.3846/jcem.2018.5189</a>

Result language

angličtina

Original language name

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

Original language description

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.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10102 - Applied mathematics

Project

Result was created during the realization of more than one project. More information in the Projects tab.

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2018

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Journal of civil engineering and management

ISSN

1392-3730

e-ISSN

1822-3605

Volume of the periodical

24

Issue of the periodical within the volume

5

Country of publishing house

LT - LITHUANIA

Number of pages

14

Pages from-to

410-423

UT code for WoS article

000446022400005

EID of the result in the Scopus database

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